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High School Math : Basic Single-Variable Algebra

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Equations

Solve the following equation for :

9x + 3x + 2 + 10 = 4(2+x)

Possible Answers:

x = -2

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

x = 2

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

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

Correct answer:

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

Explanation:

9x + 3x + 2 + 10 = 4(2+x)

The first step to solve this equation is expand out the right-hand side of the equation by multiplying the 4 through the parentheses:

$9x + 3x + 2 + 10 = 4\cdot 2+4\cdot x$

9x + 3x + 2 + 10 = 8+4x

Next, we combine like terms. That is, we put all of the terms with an on one side of the equation and all the terms without on the other. We'll start by subtracting from both sides:

9x + 3x + 2 + 10 - 4x = 8+4x -4x

9x + 3x + 2 + 10 - 4x = 8

And now we'll move the non- terms to the right-hand side by subtracting 2 and 10 from both sides:

9x + 3x + 2 + 10 - 4x -2 -10 = 8 -2 -10

9x + 3x - 4x = 8 -2 -10

Combining these terms, this simplifies to:

8x=-4

Next, we divide both sides by 8:

$\frac{8x}{8}=\frac{-4}{8}$

Which gives:

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

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Example Question #22 : Equations

Solve the following equation for y:

$\frac{y}{2} + 3 = -7$

Possible Answers:

y = 5

y = 20

y = 10

y = -20

y = -5

Correct answer:

y = -20

Explanation:

$\frac{y}{2} + 3 = -7$

The first step in solving this equation it to subtract 3 from both sides, so that the term with is alone on one side of the equals sign.

$\frac{y}{2} + 3 -3 = -7-3$

which simplifies to:

$\frac{y}{2} = -10$

From here, we multiply both sides by 2:

$2\cdot \frac{y}{2} = -10\cdot 2$

This gives:

y = -20

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Example Question #23 : Equations

Solve the following equation for :

3x+4x+2=5x+6

Possible Answers:

x=-4

x=-2

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

x=4

x=2

Correct answer:

x=2

Explanation:

3x+4x+2=5x+6

The first step to solving this equation is to combine the terms with in them on the left-hand side of the equation. This gives:

7x+2=5x+6

Next, we can subtract from both sides of the equation:

7x+2-5x=5x+6-5x

Which simplifies to:

2x+2=6

Then, we subtract 2 from both sides of the equation:

2x+2-2=6-2

2x=4

And to finish, we now divide both sides by 2:

$\frac{2x}{2}=\frac{4}{2}$

Which simplifies to:

x = 2

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Example Question #24 : Equations

Solve the following equation for :

$\frac{x}{3}+3(x+2)=7+x$

Possible Answers:

$x=-\frac{3}{7}$

x=5

$x=\frac{3}{7}$

$x=-\frac{1}{5}$

$x=\frac{7}{3}$

Correct answer:

$x=\frac{3}{7}$

Explanation:

$\frac{x}{3}+3(x+2)=7+x$

The first step in solving this equation is to distribute the 3 through the parentheses on the left-hand side of the equation:

$\frac{x}{3}+3\cdot x+3\cdot 2=7+x$

Which gives:

$\frac{x}{3}+3x+6=7+x$

Now, in order to get rid of the fraction, we can multiply the whole equation by 3:

x+9x+18=21+3x

We can now combine the like terms on the left-hand side, which gives:

10x+18=21+3x

Now, we subtract from both sides:

10x+18-3x=21+3x-3x

7x+18=21

Next, we subtract 18 from both sides:

7x+18-18=21-18

7x=3

Last, we divide both sides by 7 to solve for :

$\frac{7x}{7}=\frac{3}{7}$

Which gives,

$x=\frac{3}{7}$

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Example Question #21 : Basic Single Variable Algebra

Solve the following equation for .

6x - 2 = -14

Possible Answers:

Correct answer:

Explanation:

To begin, we add 2 on both sides. We get 6x = -12 . Dividing by 6 we get x = -2 .

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Example Question #214 : Algebra Ii

Solve:

2x-3y=13

x+3y=-7

Possible Answers:

(5,2)

(2,3)

(2,-3)

(3,-2)

(-3,5)

Correct answer:

(2,-3)

Explanation:

Add the two equations together to get 3x=6 . Then divide by to get x=2 .

Now substitute this value into one of the original equations to get 2+3y=-7 .

Next subtract from both sides to get 3y=-9 .

Now divide both sides by to get y=-3 .

Therefore the answer is (2,-3) .

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Example Question #27 : Equations

Lilac paint is made by mixing one part blue paint and one part red pain with two parts white paint. How many gallons of white paint should be mixed with two quarts of blue paint?

Possible Answers:

$0.75\; gallon$

$0.50\; gallon$

$1.00\; gallon$

$1.50\; gallons$

$1.25\; gallons$

Correct answer:

$1.00\; gallon$

Explanation:

Set up a proportion where number of quarts of white paint.

$\frac{white}{blue} = \frac{x\; qt}{2\; qt}= \frac{2}{1}$ and solve by cross multiplying to get $x=4\; quarts$ , and $4 \; quarts = 1\; gallon$ .

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Example Question #21 : Solving Equations

What number is $125\%$ of 160 ?

Possible Answers:

200

240

225

185

300

Correct answer:

200

Explanation:

For percentage problems look for verbal cues:

"IS" means equals.

"OF" means multiplication.

Therefore the equation becomes n=1.25(160)=200 .

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Example Question #22 : Equations

An art show wants to focus on sculpture but will also accept paintings and drawings. The show has room for 140 pieces and will display them in a ratio of scupltures to painting to drawings. How many sculptures will be displayed?

Possible Answers:

Correct answer:

Explanation:

Since the paintings and the drawings have the same ratio, they will have the same number on display.

Let number of paintings displayed = number of drawings displayed.

Then, 140 - 2x = number of sculptures displayed.

Set up a proportion:

$\frac{sculptures}{drawings}=\frac{140 - 2x}{x}=\frac{3}{2}$

Solve by cross multiplying to get 2(140-2x)=3x or 280 - 4x = 3x .

Then add to both sides to get 280 = 7x .

Then divide by to get x=40 .

So there are drawings and paintings in the show, leaving the last spots for sculptures.

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Example Question #22 : Solving Equations

What number is $125\%$ of 240 ?

Possible Answers:

300

325

340

365

285

Correct answer:

300

Explanation:

Verbal cues include "IS" means equal and "OF" means multiplication.

So the equation to solve becomes $n=1.25\cdot 240=300$

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High School Math : Basic Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #21 : Equations

Example Question #22 : Equations

Example Question #23 : Equations

Example Question #24 : Equations

Example Question #21 : Basic Single Variable Algebra

Example Question #214 : Algebra Ii

Example Question #27 : Equations

Example Question #21 : Solving Equations

Example Question #22 : Equations

Example Question #22 : Solving Equations

All High School Math Resources

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