Mixing
Getting wrong answer for absolute value inequality and not sure why
$begingroup$
The question:
The function p is defined by $-2|x+4|+10$. Solve the equality $p(x) > -4$
Here were my steps to solving this:
1.) Subtract 10 from both sides -> $-2|x+4| > -14$
2.) Divide both sides by -2 -> $|x+4|>7$
3.) $x+4$ should therefore be 7 units or greater from zero on the number line, meaning either greater than 7 or less than -7:
$x+4 > 7$
$x+4 < -7$
4.) Subtract 4 from both sides:
$x > 3$
$x < -11$
Graphing this, I see my signs are the wrong way round but I'm not quite sure where I've gone wrong.
absolute-value
asked Jan 11 at 14:14
Henry CooperHenry Cooper
826
$endgroup$
|
show 2 more comments
$begingroup$
The question:
The function p is defined by $-2|x+4|+10$. Solve the equality $p(x) > -4$
Here were my steps to solving this:
1.) Subtract 10 from both sides -> $-2|x+4| > -14$
2.) Divide both sides by -2 -> $|x+4|>7$
3.) $x+4$ should therefore be 7 units or greater from zero on the number line, meaning either greater than 7 or less than -7:
$x+4 > 7$
$x+4 < -7$
4.) Subtract 4 from both sides:
$x > 3$
$x < -11$
Graphing this, I see my signs are the wrong way round but I'm not quite sure where I've gone wrong.
absolute-value
asked Jan 11 at 14:14
Henry CooperHenry Cooper
826
$endgroup$
8
$begingroup$
When you divide by a negative number, the sign needs to reverse as well.
$endgroup$
– Ininterrompue
Jan 11 at 14:16
$begingroup$
I did reverse it. -14 became 7
$endgroup$
– Henry Cooper
Jan 11 at 14:16
7
$begingroup$
Sorry. I meant the inequality sign goes from > to <.
$endgroup$
– Ininterrompue
Jan 11 at 14:17
$begingroup$
You didn’t reverse the inequality sign.
$endgroup$
– KM101
Jan 11 at 14:17
10
$begingroup$
A little tip: when you know the answer is wrong, you can find faulty steps by substituting a bad value into the previous steps. You know that the answer shouldn't include $x > 3$ as your working shows, so try substituting $x = 4$ into each step. Initially, you get a false inequality, but at the first step of bad working, it magically becomes true!
$endgroup$
– Theo Bendit
Jan 11 at 14:33
|
show 2 more comments
$begingroup$
The question:
The function p is defined by $-2|x+4|+10$. Solve the equality $p(x) > -4$
Here were my steps to solving this:
1.) Subtract 10 from both sides -> $-2|x+4| > -14$
2.) Divide both sides by -2 -> $|x+4|>7$
3.) $x+4$ should therefore be 7 units or greater from zero on the number line, meaning either greater than 7 or less than -7:
$x+4 > 7$
$x+4 < -7$
4.) Subtract 4 from both sides:
$x > 3$
$x < -11$
Graphing this, I see my signs are the wrong way round but I'm not quite sure where I've gone wrong.
absolute-value
asked Jan 11 at 14:14
Henry CooperHenry Cooper
826
$endgroup$
The question:
The function p is defined by $-2|x+4|+10$. Solve the equality $p(x) > -4$
Here were my steps to solving this:
1.) Subtract 10 from both sides -> $-2|x+4| > -14$
2.) Divide both sides by -2 -> $|x+4|>7$
3.) $x+4$ should therefore be 7 units or greater from zero on the number line, meaning either greater than 7 or less than -7:
$x+4 > 7$
$x+4 < -7$
4.) Subtract 4 from both sides:
$x > 3$
$x < -11$
Graphing this, I see my signs are the wrong way round but I'm not quite sure where I've gone wrong.
absolute-value
absolute-value
asked Jan 11 at 14:14
Henry CooperHenry Cooper
826
asked Jan 11 at 14:14
Henry CooperHenry Cooper
826
asked Jan 11 at 14:14
Henry CooperHenry Cooper
826
asked Jan 11 at 14:14
Henry CooperHenry Cooper
826
asked Jan 11 at 14:14
Henry CooperHenry Cooper
826
826
8
$begingroup$
When you divide by a negative number, the sign needs to reverse as well.
$endgroup$
– Ininterrompue
Jan 11 at 14:16
$begingroup$
I did reverse it. -14 became 7
$endgroup$
– Henry Cooper
Jan 11 at 14:16
7
$begingroup$
Sorry. I meant the inequality sign goes from > to <.
$endgroup$
– Ininterrompue
Jan 11 at 14:17
$begingroup$
You didn’t reverse the inequality sign.
$endgroup$
– KM101
Jan 11 at 14:17
10
$begingroup$
A little tip: when you know the answer is wrong, you can find faulty steps by substituting a bad value into the previous steps. You know that the answer shouldn't include $x > 3$ as your working shows, so try substituting $x = 4$ into each step. Initially, you get a false inequality, but at the first step of bad working, it magically becomes true!
$endgroup$
– Theo Bendit
Jan 11 at 14:33
|
show 2 more comments
8
$begingroup$
When you divide by a negative number, the sign needs to reverse as well.
$endgroup$
– Ininterrompue
Jan 11 at 14:16
$begingroup$
I did reverse it. -14 became 7
$endgroup$
– Henry Cooper
Jan 11 at 14:16
7
$begingroup$
Sorry. I meant the inequality sign goes from > to <.
$endgroup$
– Ininterrompue
Jan 11 at 14:17
$begingroup$
You didn’t reverse the inequality sign.
$endgroup$
– KM101
Jan 11 at 14:17
10
$begingroup$
A little tip: when you know the answer is wrong, you can find faulty steps by substituting a bad value into the previous steps. You know that the answer shouldn't include $x > 3$ as your working shows, so try substituting $x = 4$ into each step. Initially, you get a false inequality, but at the first step of bad working, it magically becomes true!
$endgroup$
– Theo Bendit
Jan 11 at 14:33
8
8
$begingroup$
When you divide by a negative number, the sign needs to reverse as well.
$endgroup$
– Ininterrompue
Jan 11 at 14:16
$begingroup$
When you divide by a negative number, the sign needs to reverse as well.
$endgroup$
– Ininterrompue
Jan 11 at 14:16
$begingroup$
I did reverse it. -14 became 7
$endgroup$
– Henry Cooper
Jan 11 at 14:16
$begingroup$
I did reverse it. -14 became 7
$endgroup$
– Henry Cooper
Jan 11 at 14:16
7
7
$begingroup$
Sorry. I meant the inequality sign goes from > to <.
$endgroup$
– Ininterrompue
Jan 11 at 14:17
$begingroup$
Sorry. I meant the inequality sign goes from > to <.
$endgroup$
– Ininterrompue
Jan 11 at 14:17
$begingroup$
You didn’t reverse the inequality sign.
$endgroup$
– KM101
Jan 11 at 14:17
$begingroup$
You didn’t reverse the inequality sign.
$endgroup$
– KM101
Jan 11 at 14:17
10
10
$begingroup$
A little tip: when you know the answer is wrong, you can find faulty steps by substituting a bad value into the previous steps. You know that the answer shouldn't include $x > 3$ as your working shows, so try substituting $x = 4$ into each step. Initially, you get a false inequality, but at the first step of bad working, it magically becomes true!
$endgroup$
– Theo Bendit
Jan 11 at 14:33
$begingroup$
A little tip: when you know the answer is wrong, you can find faulty steps by substituting a bad value into the previous steps. You know that the answer shouldn't include $x > 3$ as your working shows, so try substituting $x = 4$ into each step. Initially, you get a false inequality, but at the first step of bad working, it magically becomes true!
$endgroup$
– Theo Bendit
Jan 11 at 14:33
|
show 2 more comments
2 Answers
2
active
oldest
votes
$begingroup$
$20$ is greater than $8$, right?
$$20 > 8$$
Now divide both sides by $-2$:
$$-10 > -4$$
Whoops! That's not right. This is because when you multiply or divide an inequality by a negative number, you must change the sense of the inequality: $>$ becomes $<$, and $le$ becomes $ge$ etc:
$$-10 < -4$$
answered Jan 11 at 14:21
TonyKTonyK
42.6k355134
$endgroup$
1
$begingroup$
The glorious feeling of catharsis! Thanks Tony, I'll accept your answer in 7 minutes :)
$endgroup$
– Henry Cooper
Jan 11 at 14:22
$begingroup$
Can't help but think the example would have been clear withdivide by -1but good answer
$endgroup$
– ArtB
Jan 12 at 22:33
add a comment |
$begingroup$
$-2|x+4|>-14$ implies that $|x+4|<7$ (the greater than becomes smaller than because you multiply by a negative number).
The rest is all good.
edited Jan 11 at 17:06
Brian J
304517
answered Jan 11 at 14:17
new usernew user
1014
$endgroup$
1
$begingroup$
Did you lose your 2 somewhere in there? Or in fact gain an unwanted 2 I think...
$endgroup$
– Chris
Jan 11 at 14:47
1
$begingroup$
He meant $-14$ in the first inequality.
$endgroup$
– KM101
Jan 11 at 15:17
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$20$ is greater than $8$, right?
$$20 > 8$$
Now divide both sides by $-2$:
$$-10 > -4$$
Whoops! That's not right. This is because when you multiply or divide an inequality by a negative number, you must change the sense of the inequality: $>$ becomes $<$, and $le$ becomes $ge$ etc:
$$-10 < -4$$
answered Jan 11 at 14:21
TonyKTonyK
42.6k355134
$endgroup$
1
$begingroup$
The glorious feeling of catharsis! Thanks Tony, I'll accept your answer in 7 minutes :)
$endgroup$
– Henry Cooper
Jan 11 at 14:22
$begingroup$
Can't help but think the example would have been clear withdivide by -1but good answer
$endgroup$
– ArtB
Jan 12 at 22:33
add a comment |
$begingroup$
$20$ is greater than $8$, right?
$$20 > 8$$
Now divide both sides by $-2$:
$$-10 > -4$$
Whoops! That's not right. This is because when you multiply or divide an inequality by a negative number, you must change the sense of the inequality: $>$ becomes $<$, and $le$ becomes $ge$ etc:
$$-10 < -4$$
answered Jan 11 at 14:21
TonyKTonyK
42.6k355134
$endgroup$
1
$begingroup$
The glorious feeling of catharsis! Thanks Tony, I'll accept your answer in 7 minutes :)
$endgroup$
– Henry Cooper
Jan 11 at 14:22
$begingroup$
Can't help but think the example would have been clear withdivide by -1but good answer
$endgroup$
– ArtB
Jan 12 at 22:33
add a comment |
$begingroup$
$20$ is greater than $8$, right?
$$20 > 8$$
Now divide both sides by $-2$:
$$-10 > -4$$
Whoops! That's not right. This is because when you multiply or divide an inequality by a negative number, you must change the sense of the inequality: $>$ becomes $<$, and $le$ becomes $ge$ etc:
$$-10 < -4$$
answered Jan 11 at 14:21
TonyKTonyK
42.6k355134
$endgroup$
$20$ is greater than $8$, right?
$$20 > 8$$
Now divide both sides by $-2$:
$$-10 > -4$$
Whoops! That's not right. This is because when you multiply or divide an inequality by a negative number, you must change the sense of the inequality: $>$ becomes $<$, and $le$ becomes $ge$ etc:
$$-10 < -4$$
answered Jan 11 at 14:21
TonyKTonyK
42.6k355134
answered Jan 11 at 14:21
TonyKTonyK
42.6k355134
answered Jan 11 at 14:21
TonyKTonyK
42.6k355134
answered Jan 11 at 14:21
TonyKTonyK
42.6k355134
42.6k355134
1
$begingroup$
The glorious feeling of catharsis! Thanks Tony, I'll accept your answer in 7 minutes :)
$endgroup$
– Henry Cooper
Jan 11 at 14:22
$begingroup$
Can't help but think the example would have been clear withdivide by -1but good answer
$endgroup$
– ArtB
Jan 12 at 22:33
add a comment |
1
$begingroup$
The glorious feeling of catharsis! Thanks Tony, I'll accept your answer in 7 minutes :)
$endgroup$
– Henry Cooper
Jan 11 at 14:22
$begingroup$
Can't help but think the example would have been clear withdivide by -1but good answer
$endgroup$
– ArtB
Jan 12 at 22:33
1
1
$begingroup$
The glorious feeling of catharsis! Thanks Tony, I'll accept your answer in 7 minutes :)
$endgroup$
– Henry Cooper
Jan 11 at 14:22
$begingroup$
The glorious feeling of catharsis! Thanks Tony, I'll accept your answer in 7 minutes :)
$endgroup$
– Henry Cooper
Jan 11 at 14:22
$begingroup$
Can't help but think the example would have been clear with
divide by -1 but good answer$endgroup$
– ArtB
Jan 12 at 22:33
$begingroup$
Can't help but think the example would have been clear with
divide by -1 but good answer$endgroup$
– ArtB
Jan 12 at 22:33
add a comment |
$begingroup$
$-2|x+4|>-14$ implies that $|x+4|<7$ (the greater than becomes smaller than because you multiply by a negative number).
The rest is all good.
edited Jan 11 at 17:06
Brian J
304517
answered Jan 11 at 14:17
new usernew user
1014
$endgroup$
1
$begingroup$
Did you lose your 2 somewhere in there? Or in fact gain an unwanted 2 I think...
$endgroup$
– Chris
Jan 11 at 14:47
1
$begingroup$
He meant $-14$ in the first inequality.
$endgroup$
– KM101
Jan 11 at 15:17
add a comment |
$begingroup$
$-2|x+4|>-14$ implies that $|x+4|<7$ (the greater than becomes smaller than because you multiply by a negative number).
The rest is all good.
edited Jan 11 at 17:06
Brian J
304517
answered Jan 11 at 14:17
new usernew user
1014
$endgroup$
1
$begingroup$
Did you lose your 2 somewhere in there? Or in fact gain an unwanted 2 I think...
$endgroup$
– Chris
Jan 11 at 14:47
1
$begingroup$
He meant $-14$ in the first inequality.
$endgroup$
– KM101
Jan 11 at 15:17
add a comment |
$begingroup$
$-2|x+4|>-14$ implies that $|x+4|<7$ (the greater than becomes smaller than because you multiply by a negative number).
The rest is all good.
edited Jan 11 at 17:06
Brian J
304517
answered Jan 11 at 14:17
new usernew user
1014
$endgroup$
$-2|x+4|>-14$ implies that $|x+4|<7$ (the greater than becomes smaller than because you multiply by a negative number).
The rest is all good.
edited Jan 11 at 17:06
Brian J
304517
answered Jan 11 at 14:17
new usernew user
1014
edited Jan 11 at 17:06
Brian J
304517
edited Jan 11 at 17:06
Brian J
304517
edited Jan 11 at 17:06
Brian J
304517
304517
answered Jan 11 at 14:17
new usernew user
1014
answered Jan 11 at 14:17
new usernew user
1014
answered Jan 11 at 14:17
new usernew user
1014
1014
1
$begingroup$
Did you lose your 2 somewhere in there? Or in fact gain an unwanted 2 I think...
$endgroup$
– Chris
Jan 11 at 14:47
1
$begingroup$
He meant $-14$ in the first inequality.
$endgroup$
– KM101
Jan 11 at 15:17
add a comment |
1
$begingroup$
Did you lose your 2 somewhere in there? Or in fact gain an unwanted 2 I think...
$endgroup$
– Chris
Jan 11 at 14:47
1
$begingroup$
He meant $-14$ in the first inequality.
$endgroup$
– KM101
Jan 11 at 15:17
1
1
$begingroup$
Did you lose your 2 somewhere in there? Or in fact gain an unwanted 2 I think...
$endgroup$
– Chris
Jan 11 at 14:47
$begingroup$
Did you lose your 2 somewhere in there? Or in fact gain an unwanted 2 I think...
$endgroup$
– Chris
Jan 11 at 14:47
1
1
$begingroup$
He meant $-14$ in the first inequality.
$endgroup$
– KM101
Jan 11 at 15:17
$begingroup$
He meant $-14$ in the first inequality.
$endgroup$
– KM101
Jan 11 at 15:17
add a comment |
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8
$begingroup$
When you divide by a negative number, the sign needs to reverse as well.
$endgroup$
– Ininterrompue
Jan 11 at 14:16
$begingroup$
I did reverse it. -14 became 7
$endgroup$
– Henry Cooper
Jan 11 at 14:16
7
$begingroup$
Sorry. I meant the inequality sign goes from > to <.
$endgroup$
– Ininterrompue
Jan 11 at 14:17
$begingroup$
You didn’t reverse the inequality sign.
$endgroup$
– KM101
Jan 11 at 14:17
10
$begingroup$
A little tip: when you know the answer is wrong, you can find faulty steps by substituting a bad value into the previous steps. You know that the answer shouldn't include $x > 3$ as your working shows, so try substituting $x = 4$ into each step. Initially, you get a false inequality, but at the first step of bad working, it magically becomes true!
$endgroup$
– Theo Bendit
Jan 11 at 14:33