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ACT Math : Inequalities

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Example Questions

Example Question #5 : How To Find The Solution To An Inequality With Division

Each of the following is equivalent to

xy/z * (5(x + y)) EXCEPT:

Possible Answers:

5x² + y²/z

xy(5y + 5x)/z

5x²y + 5xy²/z

xy(5x + 5y)/z

Correct answer:

5x² + y²/z

Explanation:

Choice a is equivalent because we can say that technically we are multiplying two fractions together: (xy)/z and (5(x + y))/1. We multiply the numerators together and the denominators together and end up with xy (5x + 5y)/z. xy (5y + 5x)/z is also equivalent because it is only simplifying what is inside the parentheses and switching the order- the commutative property tells us this is still the same expression. 5x²y + 5xy²/z is equivalent as it is just a simplified version when the numerators are multiplied out. Choice 5x² + y²/z is not equivalent because it does not account for all the variables that were in the given expression and it does not use FOIL correctly.

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Example Question #6 : How To Find The Solution To An Inequality With Division

What is the solution set of the inequality $\dpi{100} \small 3x+8<35$ ?

Possible Answers:

$\dpi{100} \small x>27$

$\dpi{100} \small x<35$

$\dpi{100} \small x>9$

$\dpi{100} \small x<27$

$\dpi{100} \small x<9$

Correct answer:

$\dpi{100} \small x<9$

Explanation:

We simplify this inequality similarly to how we would simplify an equation

$\dpi{100} \small 3x+8-8<35-8$

$\dpi{100} \small \frac{3x}{3}<\frac{27}{3}$

Thus $\dpi{100} \small x<9$

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Example Question #6 : Inequalities

What is a solution set of the inequality 2x+12>42 ?

Possible Answers:

x>4

x>15

x<9

$x>\frac{3}{2}$

x<15

Correct answer:

x>15

Explanation:

In order to find the solution set, we solve 2x+12>42 as we would an equation:

2x+12>42

2x>30

x>15

Therefore, the solution set is any value of x>15 .

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Example Question #183 : Equations / Inequalities

Simplify the following inequality

$4 - 3x \ge 22 + 2x$ .

Possible Answers:

$x \ge \frac{-18}{5}$

$x \le \frac{2}{7}$

$x \ge \frac{18}{5}$

$x \ge \frac{14}{5}$

$x \le \frac{-18}{5}$

Correct answer:

$x \le \frac{-18}{5}$

Explanation:

For the most part, you can treat inequalities just like equations. (It is not exact, as you will see below.) Thus, start by isolating your variables. Subtract from both sides:

$4 - 5x \ge 22$

Next, subtract from both sides:

$- 5x \ge 18$

Finally—here you need to be careful—divide by . When you divide or multiply by a negative value in inequalities, you need to flip the inequality sign.

Thus, you get:

$x \le \frac{-18}{5}$

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Example Question #184 : Equations / Inequalities

What is the solution to the given inequality:
$-3x\geq 12$

Possible Answers:

x>-4

$x\leq -4$

$x\leq4$

$x\geq -4$

x<-4

Correct answer:

$x\leq -4$

Explanation:

When solving an inequality in which you have to mulitiply or divide by a negative number, you must "flip" the direction of the inequality. Other than that, solve it nomrally.

Thus the first and only step we have is to divide by and since that number is negative, we "flip" the inequality.

Yielding:

$\frac{-3x}{-3}\geq \frac{12}{-3}$

$x\leq -4$

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Example Question #185 : Equations / Inequalities

Solve the following inequality:

4x>2

Possible Answers:

x<8

$x<\frac{1}{2}$

x>8

$x>\frac{1}{2}$

Correct answer:

$x>\frac{1}{2}$

Explanation:

To solve, simply solve as though it is 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.

Only when dividing or multiplying by a negative number, will you have to flip the inequality sign.

4x>2

4x=2

$x=\frac{2}{4}$

$x=\frac{1}{2}$

$x>\frac{1}{2}$

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Example Question #41 : Inequalities

Solve the following inequality:

3x<27

Possible Answers:

x>3

x<9

x>9

x<3

Correct answer:

x<9

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,

$3x>27\Rightarrow \frac{3x}{3}>\frac{27}{3}\Rightarrow x>9$

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ACT Math : Inequalities

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #5 : How To Find The Solution To An Inequality With Division

Example Question #6 : How To Find The Solution To An Inequality With Division

Example Question #6 : Inequalities

Example Question #183 : Equations / Inequalities

Example Question #184 : Equations / Inequalities

Example Question #185 : Equations / Inequalities

Example Question #41 : Inequalities

All ACT Math Resources

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