PSAT Math : How to find the solution to an inequality with addition
Study concepts, example questions & explanations for PSAT Math
All PSAT Math Resources
Example Questions
Example Question #1 : How To Find The Solution To An Inequality With Addition
What values of x make the following statement true?
|x – 3| < 9
x < 12
–3 < x < 9
–12 < x < 6
6 < x < 12
–6 < x < 12
–6 < x < 12
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.
Example Question #6 : How To Find The Solution To An Inequality With Addition
If –1 < w < 1, all of the following must also be greater than –1 and less than 1 EXCEPT for which choice?
w/2
w2
3w/2
|w|
|w|0.5
3w/2
3w/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.
Example Question #7 : How To Find The Solution To An Inequality With Addition
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.
Example Question #231 : Algebra
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.
Example Question #791 : Psat Mathematics
If 
-
In order to solve this inequality, you must isolate 
Therefore, the only option that solves the inequality is 
Example Question #1 : How To Find The Solution To An Inequality With Addition
What values of 
First, solve the inequality 
Since we are dealing with absolute value, 
Certified Tutor
Certified Tutor
All PSAT Math Resources
