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High School Math : Basic Single-Variable Algebra

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Example Questions

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Example Question #1 : Solving Equations

Solve the pair of equations for x and y:

x+y=4

x-y=8

Possible Answers:

x=-6,y=-2

x=6, y=-2

x=2,y=-6

x=-2,y=6

x=-6,y=2

Correct answer:

x=6, y=-2

Explanation:

Equation 1: x+y=4

Equation 2: x-y=8

Solve equation 2 for X: x=8+y

Substitute into Equation 1: (8+y)+y=4

Solve for y: 2y=-4 , y=-2

Take the answer for y and plug it back into either original equation to find x:

x=6, y=-2

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Example Question #2 : Solving Equations

Solve the pair of equations for x and y:

2x+y=16

y-2x=0

Possible Answers:

x=-4,y=8

x=8,y=-4

x=4,y=8

x=4,y=-8

x=8,y=4

Correct answer:

x=4,y=8

Explanation:

Equation 1: 2x+y=16

Equation 2: y-2x=0

Solve Equation 2 for y:

y=2x

Substitute into Equation 1:

2x+2x=16

4x=16

x=4

Plug x back into either original equations and solve for y:

x=4,y=8

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Example Question #3 : Solving Equations

For which of the following functions is the result of f(-2) a positive integer?

Possible Answers:

5x^2 + 2

2x-5

2x-10

6x^3

2x^2-13

Correct answer:

5x^2 + 2

Explanation:

Simply plugging in -2 into each answer choice will determine the correct answer:

6x^3 = 6(-2)^3 = -48

2x-5=2(-2)-5=-9

2x^2-13=2(-2)^2-13=-5

5x^2 + 2 = 5(-2)^2 + 5 = 25

2x-10 = 2(-2) - 10 = -14

The key to solving this problem is to remember the order of operations and that negative numbers squared are positive, while negative numbers raised to the third power are negative.

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Example Question #11 : Equations

Given the equation x^3 -6 = 210 , what is the value of 2x + 3 ?

Possible Answers:

Correct answer:

Explanation:

When solving the equation x^3 - 6 = 210 , observe that x^3 = 216 . Taking the cube root of 216 gives 6. Thus, 2x + 3=2(6) + 3=15.

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Example Question #11 : Equations

A cardboard packing box contains footballs and baseballs. The ratio by weight of baseballs to footballs is 7 to 9. How many kilograms of footballs will there be in the box if the total weight of the box is 48 kilograms?

Possible Answers:

Correct answer:

Explanation:

In the box, there are kilograms of baseballs and kilograms of footballs. In total, there are 16x kilograms of balls. The total weight of the box is 48 kilograms, so $16x = 48\: and\: x = 3.$ Since there are kilograms of footballs, the total weight of the footballs in the box is equal to: 9(3) = 27.

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Example Question #11 : Equations

Solve the following equation.

5(x - 5) = 5

Possible Answers:

x = 6

x = 25

x = -6

x = 1

x = -1

Correct answer:

x = 6

Explanation:

To begin solving, we use the distributive property to simplify the left side. We get: 5x - 25 = 5 . Then, adding 25 to both sides, we get: 5x = 30 . Dividing by 5, we get that x = 6 .

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Example Question #12 : Equations

Solve the equation for .

4x + 2 = 3x - 1

Possible Answers:

No solution

x = 3

x = -1

x = -3

x = 1

Correct answer:

x = -3

Explanation:

4x + 2 = 3x - 1

Since we have variables on both sides, we first subtract from both sides.

This leaves us with x + 2 = -1 .

Subtracting 2 from both sides, we get x = -3 .

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Example Question #13 : Equations

Solve for

4(3 - y) = 6y + 2

Possible Answers:

y = 1

$y = \frac{10}{7}$

$y = \frac{1}{7}$

$y = \frac{7}{5}$

y = 5

Correct answer:

y = 1

Explanation:

4(3 - y) = 6y + 2

First, use the distributive property to multiply out the left side:

12 - 4y = 6y + 2

Then, add on both sides:

12 = 10y + 2

Subtract 2 from both sides:

10 = 10y

Divide both sides by 10 to get 1 = y , or y = 1 .

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Example Question #14 : Equations

Solve the following equation for .

2(z+3)=18

Possible Answers:

z = 7

z = 12

z = 7.5

z = 6

z = 2

Correct answer:

z = 6

Explanation:

The first step in solving this equation is to distribute the 2 through the parentheses. This gives us:

$2\cdot z + 2\cdot 3 = 18$

2z+6=18

Next, we subtract 6 from both sides, in order to get the variable alone on one side of the equation:

2z+6 - 6 =18-6

2z = 12

Finally, we divide both sides by 2 to solve for :

$\frac{2z}{2} = \frac{12}{2}$

z = 6

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Example Question #15 : Equations

Solve the following equation for :

6x + 3 = 4x - 7

Possible Answers:

x = 2

x = -5

x = 5

x = -2

x = 1

Correct answer:

x = -5

Explanation:

The first step in solving this equation is to combine the like terms. That is, move all of the terms with an in it to one side of the equation, and all the terms without an to the other side. Let's begin with moving the terms to the left side of the equation. We do this by subtracting from each side:

6x + 3 - 4x = 4x - 7 - 4x

2x+3=-7

Next, we combine the terms without an on the right side. We do this by subtracting 3 from both sides:

2x+3-3 = -7-3

2x = -10

Finally, we divide both sides of the equation by 2 to solve for :

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

x = -5

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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 #1 : Solving Equations

Example Question #2 : Solving Equations

Example Question #3 : Solving Equations

Example Question #11 : Equations

Example Question #11 : Equations

Example Question #11 : Equations

Example Question #12 : Equations

Example Question #13 : Equations

Example Question #14 : Equations

Example Question #15 : Equations

All High School Math Resources

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