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High School Math : Solving Inequalities

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Example Questions

Example Question #1 : Solving Inequalities

Solve for :

$\frac{-7x-2}{3}>11$

Possible Answers:

x>-3

x>2

x<7

x>-5

x<-5

Correct answer:

x<-5

Explanation:

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that becomes , and vice versa.

$\frac{-7x-2}{3}>11$

-7x-2>33

-7x>35

$\frac{-7x}{-7}<\frac{35}{-7}$

x<-5

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Example Question #2 : Solving Inequalities

Solve for :

x^2+4x>12

Possible Answers:

x>2

$x<-6\ and\ x>2$

x<-12

$x<-2\ and\ x>6$

x<6

Correct answer:

$x<-6\ and\ x>2$

Explanation:

So when we solve inequalities with binomials, we must create two scenarios: one where the value inside of the parentheses is positive and one where it is negative. For the negative scenario, we must flip the sign as we normally do for inequalities.

x^2+4x>12

x^2+4x+4>12+4

(x+2)^2>16

Now we must create our two scenarios:

$x+2>{\sqrt{16}}$ and $x+2<-{\sqrt{16}}$

Notice that in the negative scenario, we flipped the sign of the inequality.

x+2>4 and x+2<-4

x>2 and x<-6

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Example Question #2 : Solving Inequalities

Solve for :

x^2-10x<24

Possible Answers:

x<-12

$x>-2\ and\ x<12$

$x>0\ and\ x<2$

x>5

$x<5\ and\ x>10$

Correct answer:

$x>-2\ and\ x<12$

Explanation:

x^2-10x<24

x^2-10x+25<24+25

(x-5)^2<49

Now we must create our two scenarios:

$x-5<{\sqrt{49}}$ and $x-5>-{\sqrt{49}}$

Notice that in the negative scenario, we flipped the sign of the inequality.

x-5<7 and x-5>-7

x<12 and x>-2

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Example Question #1 : Solving Inequalities

Solve the inequality for x:

2x+4>64

Possible Answers:

x>28

x<28

x<30

x>30

x=30

Correct answer:

x>30

Explanation:

2x+4>64

Subtract 4 from both sides:

2x > 60

Divide both sides by 2:

x > 30

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Example Question #1 : Solving Inequalities

Solve for .

$-7x-4\geq10$

Possible Answers:

$x\leq-2$

$x\leq2$

$x\geq2$

$x\geq-2$

Correct answer:

$x\leq-2$

Explanation:

$-7x-4\geq10$

Add 4 to both sides.

$-7x\geq14$

Divide both sides by –7. When dividing by a negative value, we must also change the direction of the inequality sign.

$x\leq-2$

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Example Question #5 : Solving Inequalities

Solve for :

$9x-27\geq6x$

Possible Answers:

$x\geq9$

x>9

$x\leq3$

$x\leq9$

$x\geq3$

Correct answer:

$x\geq9$

Explanation:

$9x-27\geq6x$

Move like terms to the same sides:

$9x-6x\geq27$

Combine like terms:

$3x\geq27$

Divide both sides by 3:

$x\geq9$

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Example Question #4 : Solving Inequalities

Solve for :

$5-3x\leq14$

Possible Answers:

$x\geq3$

$x\geq-3$

$x\geq9$

$x\leq3$

$x\geq0$

Correct answer:

$x\geq-3$

Explanation:

$5-3x\leq14$

$-3x\leq9$

$\frac{-3x}{-3}\geq\frac{9}{-3}$

$x\geq-3$

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High School Math : Solving Inequalities

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Solving Inequalities

Example Question #2 : Solving Inequalities

Example Question #2 : Solving Inequalities

Example Question #1 : Solving Inequalities

Example Question #1 : Solving Inequalities

Example Question #5 : Solving Inequalities

Example Question #4 : Solving Inequalities

All High School Math Resources

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