ACT Math : How to find the solution to an inequality with subtraction

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Inequalities

Given that x = 2 and y = 4, how much less is the value of  2x2 –  2y than the value of  2y2 –  2x ?

Possible Answers:

28

52

2

12

Correct answer:

28

Explanation:

First, we solve each expression by plugging in the given values for x and y:

2(22) – 2(4) = 8 – 8 = 0

2(42) – 2(2) = 32 – 4 = 28

Then we find the difference between the first and second expressions’ values:

28 – 0 = 28

Example Question #1 : How To Find The Solution To An Inequality With Subtraction

Solve

Possible Answers:

Correct answer:

Explanation:

Absolute value problems are broken into two inequalities:   and .  Each inequality is solved separately to get  and .  Graphing each inequality shows that the correct answer is .

Example Question #1 : Inequalities

Which of the following inequalities defines the solution set to  ?

Possible Answers:

Correct answer:

Explanation:

First, move the s to one side.

Subtract by 1

Divide both sides by 7.

Example Question #2 : Inequalities

The cost, in cents, of manufacturing \dpi{100} \small x pencils is \dpi{100} \small 1200+20x. The pencils sell for 50 cents each. What number of pencils would need to be sold so that the revenue received is at least equal to the manufacturing cost? 

Possible Answers:

\dpi{100} \small 27

\dpi{100} \small 33

\dpi{100} \small 36

\dpi{100} \small 30

\dpi{100} \small 40

Correct answer:

\dpi{100} \small 40

Explanation:

If each pencil sells at 50 cents, \dpi{100} \small x pencils will sell at \dpi{100} \small 50x. The smallest value of \dpi{100} \small x such that

 \dpi{100} \small 50x\geq 1200+20x

\dpi{100} \small x\geq 40

Example Question #3 : Inequalities

Solve the following inequality:

Possible Answers:

Correct answer:

Explanation:

To solve an inequality with subtraction, simply solve it is as an equation.

The goal is to isolate the variable on one side with all other constants on the other side. Perform the opposite operation to manipulate the inequality.

In this case add two to each side.

Example Question #4 : Inequalities

Solve the following inequality:

Possible Answers:

Correct answer:

Explanation:

To solve, simply treat it as an equation.

This means you want to isolate the variable on one side and move all other constants to the other side through opposite operation manipulation.

Remember, you only flip the inequality sign if you multiply or divide by a negative number.

Thus,

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: