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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #56 : Solving Inequalities

Solve the inequality: $-8x+40\geq -5x-20$

Possible Answers:

$x\leq -\frac{20}{13}$

$x\leq \frac{20}{3}$

$x\leq -20$

$x\leq \frac{20}{13}$

$x\leq 20$

Correct answer:

$x\leq 20$

Explanation:

Add on both sides of the inequality.

$-8x+40+(8x)\geq -5x-20+(8x)$

Simplify both sides.

$40\geq 3x-20$

Add 20 on both sides.

$40+20\geq 3x-20+20$

$60\geq3x$

Divide by three on both sides.

$\frac{60}{3}\geq\frac{3x}{3}$

$20\geq x$

The answer is: $x\leq 20$

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Example Question #57 : Solving Inequalities

Solve the inequality: $5x-8\geq -82$

Possible Answers:

$x\geq-\frac{74}{5}$

x<-18

$x\leq-18$

$x\leq-\frac{74}{5}$

$x\geq-18$

Correct answer:

$x\geq-\frac{74}{5}$

Explanation:

Add 8 on both sides.

$5x-8+8\geq -82+8$

$5x\geq -74$

Divide by five on both sides. It is not necessary to switch the direction of the sign.

$\frac{5x}{5}\geq \frac{-74}{5}$

Simplify both sides.

The answer is: $x\geq-\frac{74}{5}$

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Example Question #58 : Solving Inequalities

Solve the inequality: 6x-9>81-3x

Possible Answers:

x>-30

x<-18

x>30

x>10

x>-18

Correct answer:

x>10

Explanation:

Add on both sides.

6x-9+3x>81-3x+3x

9x-9>81

Add nine on both sides.

9x-9+9>81+9

9x>90

Divide by nine on both sides.

$\frac{9x}{9}>\frac{90}{9}$

The answer is: x>10

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Example Question #55 : Solving Inequalities

Solve the inequality: -5x+3>-6x+18

Possible Answers:

$x>-\frac{15}{11}$

x<15

$x<-\frac{15}{11}$

$x>-\frac{11}{15}$

x>15

Correct answer:

x>15

Explanation:

Add on both sides.

-5x+3+6x>-6x+18+6x

Simplify both sides.

x+3>18

Subtract 3 on both sides.

x+3-3>18-3

The answer is: x>15

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Example Question #56 : Solving Inequalities

Solve the inequality: -3(x-6)>-15

Possible Answers:

x>11

x<-1

x>-1

x<11

x<-11

Correct answer:

x<11

Explanation:

Divide by negative three on both sides. This operation will require changing the signs.

$\frac{-3(x-6)}{-3}>\frac{-15}{-3}$

x-6<5

Add 6 on both sides.

x-6+6<5+6

The answer is: x<11

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Example Question #61 : Solving Inequalities

Find the solution space for the inequality below:

5-4x>17

Possible Answers:

x>3

x>-3

x<-3

x<3

Correct answer:

x<-3

Explanation:

We begin solving the inequality the same way that we would solve an equality, we work to get x by itself.

5-4x>17 (subtract 5 from both sides)

-4x>12 (divide both sides by (-4) and FLIP THE INEQUALITY)

x<-3 (this is the solution space)

The key to solving this problem which is easy to forget is to FLIP THE INEQUALITY SYMBOL.

The reason we did this is because the sign changed on both sides.

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Example Question #61 : Solving Inequalities

Solve the inequality: $4x-6\geq11x+4$

Possible Answers:

$x\geq -\frac{7}{10}$

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

$x\geq -\frac{10}{7}$

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

$x\leq -\frac{10}{7}$

Correct answer:

$x\leq -\frac{10}{7}$

Explanation:

Subtract on both sides.

$4x-6-4x\geq11x+4-4x$

$-6\geq7x+4$

Subtract four on both sides.

$-6-4\geq7x+4-4$

Simplify both sides.

$-10\geq7x$

Divide by seven on both sides.

$\frac{-10}{7}\geq\frac{7x}{7}$

$-\frac{10}{7} \geq x$

The answer is: $x\leq -\frac{10}{7}$

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Example Question #63 : Solving Inequalities

Solve the inequality: 5(-3x+2)>-5x

Possible Answers:

x<-1

x>-1

x>1

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

x<1

Correct answer:

x<1

Explanation:

Distribute the five through the binomial.

5(-3x)+5(2)>-5x

Simplify the inequality.

-15x+10>-5x

Add 15x on both sides.

-15x+10+15x>-5x+15x

10>10x

Divide by ten on both sides.

1>x

The answer is: x<1

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Example Question #62 : Solving Inequalities

Solve the inequality: 5(3x-3)>8x

Possible Answers:

$x<\frac{15}{7}$

$x>\frac{23}{15}$

$x>-\frac{15}{7}$

$x>\frac{15}{7}$

$x<\frac{23}{15}$

Correct answer:

$x>\frac{15}{7}$

Explanation:

Simplify the left side of 5(3x-3)>8x using distribution.

15x-15>8x

Subtract on both sides.

15x-15-8x>8x-8x

7x-15>0

Add 15 on both sides.

7x-15+15>0+15

7x>15

Divide by seven on both sides.

$\frac{7x}{7}>\frac{15}{7}$

The answer is: $x>\frac{15}{7}$

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Example Question #65 : Solving Inequalities

Solve the inequality: $3(3-4x)\leq 26x-2$

Possible Answers:

$x\geq -\frac{7}{38}$

$x\geq -\frac{11}{14}$

$x\geq -\frac{11}{38}$

$x\geq \frac{11}{14}$

$x\geq \frac{11}{38}$

Correct answer:

$x\geq \frac{11}{38}$

Explanation:

Simplify the left side of the inequality. Distribute the three across both terms in the binomial.

$3(3-4x)\leq 26x-2$

$9-12x\leq 26x-2$

Add 12x on both sides.

$9-12x+12\leq 26x-2+12x$

$9\leq 38x-2$

Add 2 on both sides of the equation.

$9+2\leq 38x-2+2$

$11\leq 38x$

Divide by 38 on both sides.

$\frac{11}{38}\leq \frac{38x}{38}$

$\frac{11}{38}\leq x$

The answer is: $x\geq \frac{11}{38}$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #56 : Solving Inequalities

Example Question #57 : Solving Inequalities

Example Question #58 : Solving Inequalities

Example Question #55 : Solving Inequalities

Example Question #56 : Solving Inequalities

Example Question #61 : Solving Inequalities

Find the solution space for the inequality below:

Example Question #61 : Solving Inequalities

Example Question #63 : Solving Inequalities

Example Question #62 : Solving Inequalities

Example Question #65 : Solving Inequalities

All Algebra II Resources

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