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Algebra 1 : Linear Equations

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Example Questions

Example Question #551 : Linear Equations

Solve for :

4 (x +7) + 2 = 5 (x + 4) - x

Possible Answers:

There is no solution.

x = 1

x = 0

can be any real number.

x = 10

Correct answer:

There is no solution.

Explanation:

4 (x +7) + 2 = 5 (x + 4) - x

$4 \cdot x +4 \cdot 7 + 2 = 5 \cdot x + 5 \cdot 4 - x$

4 x +28+ 2 = 5x + 20- x

4 x +30 = 4x + 20

30 = 20

This identically false statement is an indication that there is no solution.

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Example Question #552 : Linear Equations

Solve for :

4 (x +9) + 9 = 5 (x + 9) - x

Possible Answers:

x=0

x=45

There is no solution.

can be any real number.

x=1

Correct answer:

can be any real number.

Explanation:

4 (x +9) + 9 = 5 (x + 9) - x

$4 \cdot x +4 \cdot 9 + 9 = 5 \cdot x + 5 \cdot 9 - x$

4 x +36 + 9 = 5x + 45 - x

4 x + 45 = 4x + 45

This identically true statement is an indication that the solution set is the set of all real numbers.

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Example Question #553 : Linear Equations

Solve for :

S = 4pk + 9

Possible Answers:

$p = \frac{S-9}{4k}$

$p = \frac{9-S}{4k}$

$p = \frac{S}{4k} + 9$

$p = 9 - \frac{S}{4k}$

$p = \frac{S+9}{4k}$

Correct answer:

$p = \frac{S-9}{4k}$

Explanation:

4pk + 9 = S

4pk + 9 -9 = S -9

4pk = S -9

$4pk \div 4k = \left (S -9 \right ) \div 4k$

$p = \frac{S-9}{4k}$

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Example Question #554 : Linear Equations

Solve for :

A = 7X -6Y

Possible Answers:

$X = \frac{A- 6Y}{7}$

$X = \frac{6Y-A}{7}$

$X = \frac{A}{7}- 6Y$

$X = \frac{A}{7}+ 6Y$

$X = \frac{A+ 6Y}{7}$

Correct answer:

$X = \frac{A+ 6Y}{7}$

Explanation:

7X -6Y = A

7X -6Y + 6Y = A+ 6Y

7X = A+ 6Y

$7X \div 7 = \left (A+ 6Y \right ) \div 7$

$X = \frac{A+ 6Y}{7}$

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Example Question #21 : How To Solve Two Step Equations

Solve for :

A = 5X + 6Y

Possible Answers:

$Y = \frac{A}{6}- 5X$

$Y = \frac{5X- A}{6}$

$Y = \frac{A- 5X}{6}$

$Y = \frac{A}{6}+ 5X$

$Y = \frac{A+ 5X}{6}$

Correct answer:

$Y = \frac{A- 5X}{6}$

Explanation:

5X + 6Y = A

5X + 6Y - 5X= A- 5X

6Y = A- 5X

$6Y \div 6= \left (A- 5X \right )\div 6$

$Y = \frac{A- 5X}{6}$

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Example Question #556 : Linear Equations

Solve for :

2x+9-x=6x-3x-1

Possible Answers:

Correct answer:

Explanation:

Simplify 2x+9-x=6x-3x-1 by combining like terms to get x+9=3x-1 . Subtract and add to both sides to get 10=2x . Divide both sides by 2 to get x=5 .

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Example Question #25 : How To Solve Two Step Equations

Solve the following equation for :

2x-13=9

Possible Answers:

x=2

x=-2

x=9

x=11

x=44

Correct answer:

x=11

Explanation:

This equation takes two steps to solve. When solving two steps, first we simplify the addition and subtraction terms. Then we do the multiplication/division step.

So, in 2x-13=9 , our first step is to negate the subtraction of 13. The inverse of subtracting by 13 is to add by 13. So step 1 is to add 13 to both sides. We have

2x-13=9

+13=+13

2x=22

From here, we do a second step to solve for , by doing the inverse of multiplying by 2. The inverse of multiplication is division. So to "get rid" of the 2, we divide both sides by 2. So from,

$2x=22 \rightarrow \frac{2x}{2}= \frac{22}{2}\rightarrow x= 11$

And that is our answer, x=11 .

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Example Question #557 : Linear Equations

Solve for :

5x+7=3(x+5)

Possible Answers:

Correct answer:

Explanation:

To solve for , you must first use the distributive property to simplify the right side of the equation. This gives you $\ 5x+7=3x+15$ .

Then, subtract and from both sides of the equation to get 2x=8 .

Divide both sides by and you will get a solution of x=4 .

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Example Question #558 : Linear Equations

Solve for $\small x$ .

3x+2=-7

Possible Answers:

x=0

x=-3

x=-7

x=5

$x=-\frac{5}{3}$

Correct answer:

x=-3

Explanation:

3x+2=-7

First, subtract 2 from both sides.

3x+2-2=-7-2

3x=-9

Divide both sides by 3.

$\frac{3x}{3}=\frac{-9}{3}$

x=-3

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Example Question #21 : How To Solve Two Step Equations

Solve for : 3x+5=29

Possible Answers:

$\frac{34}{3}$

Correct answer:

Explanation:

3x+5-5=29-5

3x=24

$\frac{3x}{3}=\frac{24}{3}$

x=8

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #551 : Linear Equations

Example Question #552 : Linear Equations

Example Question #553 : Linear Equations

Example Question #554 : Linear Equations

Example Question #21 : How To Solve Two Step Equations

Example Question #556 : Linear Equations

Example Question #25 : How To Solve Two Step Equations

Example Question #557 : Linear Equations

Example Question #558 : Linear Equations

Example Question #21 : How To Solve Two Step Equations

All Algebra 1 Resources

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