Solving Inequalities – ACT Math
Inequalities – Inequality problems on the ACT Math Exam will have a less than or greater than sign.
There may often be more than one inequality or equation in a single problem on the math part of the test.
The second equation may have the equal sign rather than an inequality sign, as in the examples in the next section.
Solving Inequalities – Practice Exercises
Have a look at the inequality problems below.
In the equations below, x represents the cost of one online game and y represents the cost of one discounted movie ticket.
If x − 2 > 5
and y = x − 2
Then the cost of 2 discounted movie tickets is greater than which one of the following?
A. x − 2
B. x − 5
C. y + 5
The correct answer is E.
For problems like this, look to see if both of the equations have any variables or terms in common.
In this problem, both equations contain x − 2.
The cost of one movie ticket is represented by y and y is equal to x − 2.
Therefore, we can substitute values from one equation to another.
x − 2 > 5
y > 5
If two tickets are being purchased, we need to solve for 2y.
y × 2 > 5 × 2
2y > 10
If x – 1 > 0 and y = x – 1, then y > ?
B. x + 1
C. x – 1
The correct answer is E .
Notice that both equations contain x – 1.
Therefore, we can substitute y for x – 1 in the first equation.
x – 1 > 0
x – 1 = y
y > 0