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Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #121 : Solving 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 #122 : Solving Equations

Solve for .

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

Possible Answers:

150

160

110

140

120

Correct answer:

140

Explanation:

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

x=140

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Example Question #603 : Basic Single Variable Algebra

Solve for .

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

Possible Answers:

192

320

268

212

300

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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Example Question #125 : Solving Equations

If a 10-foot ladder is leaned against a wall, the height of the ladder up the wall is given by

$h(x)=\sqrt{100-x^2}$ ,

where is the distance along the floor from the base of the ladder to the wall.

How far from the wall should the base of the ladder be in order for the ladder to reach 8 feet off the floor?

Possible Answers:

6.5

Correct answer:

Explanation:

Step 1: Plug in 8 for h(x)

$8=\sqrt{100-x^2}$

Step 2: Square both sides

64=100-x^2

Step 3: Combine like terms

x^2=36

Step 4: Solve.

x=6

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Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #121 : Solving Equations

Example Question #253 : Equations

Example Question #122 : Solving Equations

Example Question #603 : Basic Single Variable Algebra

Example Question #255 : Equations

Example Question #604 : Basic Single Variable Algebra

Example Question #257 : Equations

Example Question #258 : Equations

Example Question #259 : Equations

Example Question #125 : Solving Equations

All Algebra II Resources

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