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Algebra II : Solving Inequalities

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Example Question #31 : Solving Inequalities

Solve for .

$-\frac{x}{2}<4$

Possible Answers:

x>-2

x>-8

x<-2

x>2

x<-8

Correct answer:

x>-8

Explanation:

$-\frac{x}{2}<4$ Multiply on both sides. Remember to FLIP the inequality.

x>-8

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Example Question #32 : Solving Inequalities

Solve for .

$-\frac{3x}{5}-15< 12$

Possible Answers:

x=-45

x<-45

x>-45

x<-27

x>-27

Correct answer:

x>-45

Explanation:

$-\frac{3x}{5}-15<12$ Add on both sides.

$-\frac{3x}{5}<27$ Multiply $\frac{5}{3}$ on both sides. Remember to FLIP the inequality sign. If you try to multiply both sides by $-\frac{5}{3}$ , you will have the wrong answer. When dealing with inequality equations, always multiply or divide the positive number in front of the variable.

x>-45

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Example Question #33 : Solving Inequalities

Solve for .

$-3(x+1)\leq21$

Possible Answers:

$x\leq8$

$x\geq -8$

$x\leq-8$

$x\geq8$

x=-8

Correct answer:

$x\geq -8$

Explanation:

$-3(x+1)\leq21$ Distribute. If you decide to divide both sides by , you will change the answer. When dealing with inequalities, distribute first.

$-3x-3\leq21$ Add on both sides.

$-3x\leq24$ Divide on both sides. Remember to FLIP the inequality sign.

$x\geq-8$

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Example Question #31 : Solving Inequalities

Solve for .

$x^2\leq9$

Possible Answers:

$-3\leq x \leq3$

$-3\geq x$ or $x\geq 3$

-3>x or x>3

-3<x<3

$\pm3$

Correct answer:

$-3\leq x \leq3$

Explanation:

$x^2\leq 9$ Anytime you exponents in inequalities, you need to think of ranges of values that are acceptable. Remember, when an exponent is squared, negative values are also acceptable since two negatives multiplied are positive. We take the square root of both sides.

$x= \pm3$ Now, we need to know how to make the range for . We know if is $\pm2$ , this will satisfy the inequality since is less than . Also, $\pm2$ is between -3, 3 . Our final answer is $-3\leq x \leq3$ .

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Example Question #32 : Solving Inequalities

x^2>9

Possible Answers:

x>9 or x<-9

$x=\pm3$

-9<x<9

x>3 or x<-3

-3<x<3

Correct answer:

x>3 or x<-3

Explanation:

x^2> 9 Anytime you exponents in inequalities, you need to think of ranges of values that are acceptable. Remember, when an exponent is squared, negative values are also acceptable since two negatives multiplied are positive. We take the square root of both sides.

$x= \pm3$ Now, we need to know how to make the range for . We know if is $\pm4$ , this will satisfy the inequality since is greater than . So then we know 4>3 and -3>-4 . Our final answer is x>3 or x<-3 .

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Example Question #31 : Solving Inequalities

Solve for x: $2x - 7 \leq -1$

Possible Answers:

$x \leq -3$

$x \geq 4$

$x \leq -3$

$x \leq 4$

$x \geq 3$

Correct answer:

$x \leq 4$

Explanation:

Solve the way you would solve an equation. First add 7 to both sides

$2x \leq 8$ now divide both sides by 2

$x \leq 4$

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Example Question #37 : Solving Inequalities

Solve for x:

-2x+4<10

Possible Answers:

x<3

x>-3

x>-7

x<-3

x>3

Correct answer:

x>-3

Explanation:

-2x+4<10

First subtract 4 from both sides to isolate the variable:

-2x<6

Next divide both sides by -2. Flip the inequality when dividing or multiplying by a negative number.

x>-3

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Example Question #38 : Solving Inequalities

Solve the following inequality:

$\small -x+10>20$

Possible Answers:

No solution

$\small x>10$

$\small x>-10$

$\small x<10$

$\small \small x<-10$

Correct answer:

$\small \small x<-10$

Explanation:

To simply this you must get the x-variable by itself. The first step is to bring the 10 to the other side by subtraction.

So:

$\small -x>10$

The next step is to divide by negative one, the important part of this is to flip the sign from ">" to "<"

So:

$\small x<-10$

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Example Question #32 : Solving Inequalities

Solve the following inequality:

$-y+2\leq2$

Possible Answers:

$y\leq1$

$y\leq0$

$y\geq0$

$y\geq1$

$y\geq-1$

Correct answer:

$y\geq0$

Explanation:

This is a two-step inequality where you need to isolate "y." To do this you must first subtract 2 from both sides and then divide by negative one.

Upon doing this you get:

$y\geq \frac{0}{-1}= y\geq0$

The sign needs to be flipped because you are dividing by a negative number.

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Example Question #33 : Solving Inequalities

Solve for x:

$1< -\frac{x+5}{3}< 10$

Possible Answers:

-35<x<-8

-35> x> -8

x<-35

35> x> 8

Correct answer:

-35<x<-8

Explanation:

To solve the inequality, we must first multiply both sides of the inequality by -3. Doing this flips both of the inequalities because we are multiplying by a negative number:

-3>x+5>-30

Now, subtract 5 from both sides:

-35<x<-8

Note that rewriting it in this way is a little more clear than simply subtracting 5 from both sides and not changing anything!

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Algebra II : Solving Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #31 : Solving Inequalities

Example Question #32 : Solving Inequalities

Example Question #33 : Solving Inequalities

Example Question #31 : Solving Inequalities

Example Question #32 : Solving Inequalities

Example Question #31 : Solving Inequalities

Example Question #37 : Solving Inequalities

Example Question #38 : Solving Inequalities

Example Question #32 : Solving Inequalities

Example Question #33 : Solving Inequalities

All Algebra II Resources

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