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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #251 : Equations

Solve for .

16x=272

Possible Answers:

Correct answer:

Explanation:

16x=272 Divide on both sides.

x=17

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Example Question #252 : Equations

Solve for .

-23x=1219

Possible Answers:

Correct answer:

Explanation:

-23x=1219 Divide on both sides.

x=-53

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Example Question #253 : Equations

Solve for

-7(8-x)=3x

Possible Answers:

Correct answer:

Explanation:

-7(8-x)=3x Distribute to each term in the parenthesis.

-56+7x=3x Subtract on both sides.

-56=-4x Divide on both sides.

14=x

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Example Question #253 : Equations

Solve for .

$\frac{x}{5}=28$

Possible Answers:

120

160

150

140

110

Correct answer:

140

Explanation:

$\frac{x}{5}=28$ Multiply on both sides.

x=140

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Example Question #254 : Equations

Solve for .

$\frac{4}{5}x=240$

Possible Answers:

268

300

192

212

320

Correct answer:

300

Explanation:

$\frac{4}{5}x=240$ Multiply $\frac{5}{4}$ on both sides.

x=300

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Example Question #255 : Equations

Solve for .

$\frac{5}{x}=30$

Possible Answers:

$\frac{1}{6}$

150

$\frac{50}{9}$

$\frac{1}{30}$

Correct answer:

$\frac{1}{6}$

Explanation:

$\frac{5}{x}=30$ Cross multiply.

5=30x Divide on both sides.

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

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Example Question #604 : Basic Single Variable Algebra

Solve for .

x+43.56=89.23

Possible Answers:

36.97

55.34

23.89

45.77

45.67

Correct answer:

45.67

Explanation:

x+43.56=89.23 Subtract 43.56 on both sides.

x=45.67

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Example Question #257 : Equations

Solve for in the linear equation.

10-20x = 12x+2

Possible Answers:

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

$x = \frac{1}{4}$

x = 4

$x = \frac{1}{3}$

x = 2

Correct answer:

$x = \frac{1}{4}$

Explanation:

To solve for the variable in the linear equation, isolate the variable on one side of the equation with all other constants on the other side. To accomplish this, perform opposite operations when manipulating the equation.

First, add 20x to both sides.

10-20x = 12x +2

${\color{Red} +20x }$ ${\color{Red} +20x }$

Next subtract 2 from both sides.

10=32x+2

${\color{Red} -2 }$ ${\color{Red} -2 }$

Divide both sides by 32.

$\frac{8}{32} = \frac{32x}{32}$

$x = \frac{1}{4}$

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Example Question #258 : Equations

Solve the equation for b

$\frac{x}{y} = -abc$

Possible Answers:

$b = -\frac{acx}{y}$

$b = -\frac{y}{acx}$

$b = \frac{acy}{x}$

$b = -\frac{x}{acy}$

$b=\frac{xy}{ac}$

Correct answer:

$b = -\frac{x}{acy}$

Explanation:

In order to isolate b, divide both sides by -ac which is called $--> \frac{x}{y}(\frac{{\color{Red} 1}}{{\color{Red} -ac}}) = {-abc}(\frac{{\color{Red} 1}}{{\color{Red} -ac}}) --> b = -\frac{x}{acy}$ i operations.

$\frac{x}{y} = -abc$ $--> \frac{x}{y}(\frac{1}{-ac}) = {-abc}(\frac{1}{-ac}) --> b = -\frac{x}{acy}$

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Example Question #259 : Equations

Solve for b in the rational equation

$\frac{20}{10+b}= \frac{1}{b}$

Possible Answers:

$b = \frac{19}{10}$

$b = \frac{10}{21}$

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

$b=\frac{3}{4}$

$b = \frac{10}{19}$

Correct answer:

$b = \frac{10}{19}$

Explanation:

To solve this, use inverse and opposite properties:

Multiply both sides by b: $\frac{20}{10+b}= \frac{1}{b}$ $\Rightarrow (\frac{20}{10+b}){\color{Red} b} = \frac{1}{b}(\frac{{\color{Red} b}}{{\color{Red} 1}})$

Multiply both sides by 10+b:

$(\frac{20b}{10+b})(\frac{{\color{Red} 10+b}}{{\color{Red} 1}})= 1({\color{Red} 10+b}) \Rightarrow 20b = 10+b$

Subtract b from both sides: $20b -{\color{Red} (b)}= (10+b)-{\color{Red} (b)} -> 19b=10$

Finally divide both sides by 19 yielding: $b = \frac{10}{19}$

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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #251 : Equations

Example Question #252 : Equations

Example Question #253 : Equations

Example Question #253 : Equations

Example Question #254 : Equations

Example Question #255 : Equations

Example Question #604 : Basic Single Variable Algebra

Example Question #257 : Equations

Example Question #258 : Equations

Example Question #259 : Equations

All Algebra II Resources

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