How to find the solution to an inequality with addition - PSAT Math
Card 0 of 6
What values of x make the following statement true?
|x – 3| < 9
What values of x make the following statement true?
|x – 3| < 9
Solve the inequality by adding 3 to both sides to get x < 12. Since it is absolute value, x – 3 > –9 must also be solved by adding 3 to both sides so: x > –6 so combined.
Solve the inequality by adding 3 to both sides to get x < 12. Since it is absolute value, x – 3 > –9 must also be solved by adding 3 to both sides so: x > –6 so combined.
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Solve for 
.
Solve for
Absolute value problems always have two sides: one positive and one negative.
First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.
Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).
We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.
Absolute value problems always have two sides: one positive and one negative.
First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.
Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).
We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.
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If –1 < w < 1, all of the following must also be greater than –1 and less than 1 EXCEPT for which choice?
If –1 < w < 1, all of the following must also be greater than –1 and less than 1 EXCEPT for which choice?
3_w_/2 will become greater than 1 as soon as w is greater than two thirds. It will likewise become less than –1 as soon as w is less than negative two thirds. All the other options always return values between –1 and 1.
3_w_/2 will become greater than 1 as soon as w is greater than two thirds. It will likewise become less than –1 as soon as w is less than negative two thirds. All the other options always return values between –1 and 1.
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If 
and 
, then which of the following could be the value of 
?
If
To solve this problem, add the two equations together:
The only answer choice that satisfies this equation is 0, because 0 is less than 4.
To solve this problem, add the two equations together:
The only answer choice that satisfies this equation is 0, because 0 is less than 4.
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If 
, which of the following could be a value of 
?
If
In order to solve this inequality, you must isolate 
on one side of the equation.
Therefore, the only option that solves the inequality is 
.
In order to solve this inequality, you must isolate
Therefore, the only option that solves the inequality is
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What values of 
make the statement 
true?
What values of
First, solve the inequality 
:
Since we are dealing with absolute value, 
must also be true; therefore:
First, solve the inequality
Since we are dealing with absolute value,
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