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Algebra 1 : Systems of Inequalities

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Example Questions

Example Question #36 : How To Find The Solution To An Inequality With Division

Solve the following inequality: -12x<-36

Possible Answers:

x>3

x<-3

x<3

x>-3

$x\leq3$

Correct answer:

x>3

Explanation:

Divide by negative twelve on both sides of the inequality.

Dividing by a negative value requires changing the direction of the sign.

$\frac{-12x}{-12}<\frac{-36}{-12}$

Simplify both sides.

The answer is: x>3

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Example Question #37 : How To Find The Solution To An Inequality With Division

Solve the inequality: $-2x>-\frac{1}{3}$

Possible Answers:

$x<-\frac{1}{6}$

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

$x>\frac{1}{6}$

$x<\frac{1}{6}$

$x<-\frac{2}{3}$

Correct answer:

$x<\frac{1}{6}$

Explanation:

Divide both sides by negative two. We will need to switch the direction of the sign.

$\frac{-2x}{-2}>\frac{-\frac{1}{3}}{-2}$

Simplify both sides and switch the sign. Rewrite the complex fraction such that dividing by a negative two is similar to multiplying by negative half.

$x< -\frac{1}{3} \cdot -\frac{1}{2}$

Multiply the fractions on the right.

The answer is: $x<\frac{1}{6}$

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Example Question #38 : How To Find The Solution To An Inequality With Division

Solve the inequality: $-\frac{1}{8}x>8$

Possible Answers:

$x>\frac{63}{8}$

x>-64

x<-1

$x\leq-64$

x<-64

Correct answer:

x<-64

Explanation:

Dividing by negative one-eighth is similar to multiplying by negative eight on both sides. Since we are dividing by a negative number, the sign will switch.

$-\frac{1}{8}x \cdot -8>8 \cdot -8$

Simplify both sides.

The answer is: x<-64

Dividing by negative one-eighth is similar to multiplying by negative eight on both sides. Since we are dividing by a negative number, the sign will switch.

$-\frac{1}{8}x \cdot -8>8 \cdot -8$

Simplify both sides.

The answer is: x<-64

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Algebra 1 : Systems of Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #36 : How To Find The Solution To An Inequality With Division

Example Question #37 : How To Find The Solution To An Inequality With Division

Example Question #38 : How To Find The Solution To An Inequality With Division

All Algebra 1 Resources

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