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Algebra 1 : Linear Equations

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Example Questions

Example Question #22 : How To Solve Two Step Equations

Solve for :

q = 5pk - 7

Possible Answers:

$k = \frac{q+7}{5p}$

$k = \frac{q-7}{5p}$

$k = \frac{q}{5p}-7$

k = 5pq+7

$k = \frac{q}{5p}+7$

Correct answer:

$k = \frac{q+7}{5p}$

Explanation:

5pk - 7 = q

5pk - 7 + 7 = q + 7

5pk = q + 7

$5pk \div 5p =\left ( q + 7 \right ) \div 5p$

$k = \frac{q+7}{5p}$

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Example Question #21 : How To Solve Two Step Equations

Solve for :

4 (x +3) + 7 = 5 (x + 5) - x

Possible Answers:

can be any real number.

There is no solution.

x = 1

x = 0

x = 6

Correct answer:

There is no solution.

Explanation:

4 (x +3) + 7 = 5 (x + 5) - x

$4 \cdot x +4 \cdot3 + 7 = 5 \cdot x + 5 \cdot 5 - x$

4 x +12 + 7 = 5x + 25 - x

4 x +19 = 4x + 25

19 = 25

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

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Example Question #563 : Algebra 1

Solve for :

4 (x +6) + 11 = 6 (x + 7) - x

Possible Answers:

x = -7

$x = 3 \frac{1}{2}$

The equation has no solution.

$x = -3 \frac{1}{2}$

x =7

Correct answer:

x = -7

Explanation:

4 (x +6) + 11 = 6 (x + 7) - x

$4 \cdot x +4 \cdot 6 + 11 = 6 \cdot x + 6 \cdot 7 - x$

4 x +24 + 11 = 6x + 42 - x

4 x +35 = 5x + 42

4 x +35 -4x -42 = 5x + 42-4x -42

-7 = x

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Example Question #563 : Linear Equations

Solve for .

x^2-7x+3=x^2-6x-2

Possible Answers:

x=-1

x=-5

x=1

x=10

x=5

Correct answer:

x=5

Explanation:

x^2-7x+3=x^2-6x-2

Notice that x^2 can be canceled out by subtracting it from both sides.

x^2-x^2-7x+3=x^2-x^2-6x-2

-7x+3=-6x-2

Now, we can isolate . First, we need to get all the variables on the same side by adding to each side.

-7x+6x+3=-6x+6x-2

-x+3=-2

Subtract from both sides.

-x+3-3=-2-3

-x=-5

Finally, multiply both sides by .

-1(-x)=-1(-5)

x=5

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Example Question #31 : How To Solve Two Step Equations

Solve for :

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

Possible Answers:

$x = -\frac{9}{10}$

x = 9

The equation has no solution.

x = -9

x = 0

Correct answer:

The equation has no solution.

Explanation:

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

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

5x - 20 + 5 x - 25 = 2 x - 8 + 8x - 28

10x - 45 = 10x - 36

10x - 45 - 10x = 10x - 36- 10x

- 45 = - 36

This statement is identically false, so the original equation has no solution.

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Example Question #565 : Linear Equations

Solve for :

$\frac{3}{4} x = \frac{5}{12} x + \frac{2}{3}$

Possible Answers:

$x = \frac{7}{4}$

$x = \frac{4}{7}$

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

x = 2

x = 3

Correct answer:

x = 2

Explanation:

$\frac{3}{4} x = \frac{5}{12} x + \frac{2}{3}$

$12 \cdot \frac{3}{4} x =12 \cdot \left ( \frac{5}{12} x + \frac{2}{3} \right )$

$\frac{12}{1} \cdot \frac{3}{4} x =\frac{12}{1}\cdot \frac{5}{12} x +\frac{12}{1}\cdot \frac{2}{3}$

$\frac{3}{1} \cdot \frac{3}{1} x =\frac{1}{1}\cdot \frac{5}{1} x +\frac{4}{1}\cdot \frac{2}{1}$

9x =5x +8

9x-5x =5x -5x +8

4x =8

$4x \div 4=8\div 4$

x = 2

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Example Question #566 : Linear Equations

Solve for :

$\frac{3}{5} x + \frac{3}{20} = \frac{4}{5}$

Possible Answers:

$x = \frac{39}{100}$

$x = \frac{4}{25}$

$x = \frac{13}{12}$

$x = \frac{19}{12}$

$x = \frac{21}{100}$

Correct answer:

$x = \frac{13}{12}$

Explanation:

$\frac{3}{5} x + \frac{3}{20} = \frac{4}{5}$

$20 \cdot \left (\frac{3}{5} x + \frac{3}{20} \right ) =20 \cdot \frac{4}{5}$

$\frac{20}{1} \cdot \frac{3}{5} x + \frac{20}{1} \cdot \frac{3}{20} =\frac{20}{1} \cdot \frac{4}{5}$

$\frac{4}{1} \cdot \frac{3}{1} x + \frac{1}{1} \cdot \frac{3}{1} =\frac{4}{1} \cdot \frac{4}{1}$

12x+3=16

12x+3-3=16-3

12x=13

$12x\div 12=13\div 12$

$x = \frac{13}{12}$

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Example Question #32 : How To Solve Two Step Equations

Solve for :

$\frac{1}{2} x - 4 = \frac{3}{10}x + \frac{2}{5}$

Possible Answers:

$x=\frac{22}{5}$

x=22

x=11

$x=\frac{11}{5}$

$x=\frac{44}{5}$

Correct answer:

x=22

Explanation:

$\frac{1}{2} x - 4 = \frac{3}{10}x + \frac{2}{5}$

$10 \cdot \left (\frac{1}{2} x - 4 \right )=10 \cdot \left ( \frac{3}{10}x + \frac{2}{ 5} \right )$

$\frac{10}{1} \cdot \frac{1}{2} x - \frac{10}{1} \cdot \frac{4}{1} \right )=\frac{10}{1} \cdot \frac{3}{10}x +\frac{10}{1} \cdot \frac{2}{ 5}$

$\frac{5}{1} \cdot \frac{1}{1} x - \frac{10}{1} \cdot \frac{4}{1} \right )=\frac{1}{1} \cdot \frac{3}{1}x +\frac{2}{1} \cdot \frac{2}{ 1}$

5x-40 = 3x+4

5x-40 -3x +40= 3x +4 -3x +40

2x=44

x=22

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Example Question #567 : Linear Equations

Solve for :

5 (x - 4) + 2 (x - 3) = 3 (x - 4) + 2 (2x - 7)

Possible Answers:

The solution set is the set of all real numbers.

x = 0

$x = \frac{26}{7}$

x = -26

x = 1

Correct answer:

The solution set is the set of all real numbers.

Explanation:

5 (x - 4) + 2 (x - 3) = 3 (x - 4) + 2 (2x - 7)

$5 \cdot x -5 \cdot 4 + 2 \cdot x - 2 \cdot 3 = 3 \cdot x - 3 \cdot 4 + 2 \cdot 2x - 2 \cdot 7$

5x - 20 + 2 x - 6 = 3x - 12 + 4x - 14

7x - 26 = 7x - 26

This statement is identically true; therefore, the solution set is the set of all real numbers.

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Example Question #568 : Linear Equations

Call the three angles of a triangle $\angle1,\angle2,\angle3$ . The measure of $\angle2$ is twenty degrees more than that of $\angle 1$ ; the measure of $\angle3$ is forty degrees less than twice that of $\angle 1$ . What is the greatest measure of any of the three angles of the triangle?

Possible Answers:

$50^{\circ }$

$120^{\circ }$

$100^{\circ }$

$60^{\circ }$

$70^{\circ }$

Correct answer:

$70^{\circ }$

Explanation:

Call the measure of $\angle1$ . Since the measure of $\angle2$ is twenty degrees more than that of $\angle 1$ , we can say that $\angle2$ has measure x + 2 0 . Since the measure of $\angle3$ is forty degrees less than twice that of $\angle 1$ , we can say that $\angle3$ has measure 2x-40 .

The sum of the measures of the three angles of a triangle is 180, so we can set up and solve an equation that sets the sum of these three expressions equal to 180:

x + (x + 20) + (2x - 40) = 180

x + x+ 2x + 20 - 40= 180

4x - 20 = 180

4x = 200

x = 50

Substitute 50 for in the other two expressions:

x + 20 = 50 + 20 = 70

$2x-40 = 2\cdot50 - 40 = 60$

The triangle has angles measuring $50^{\circ }, 60^{\circ },70^{\circ }$ , so the answer to the question is $70^{\circ }$ .

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #22 : How To Solve Two Step Equations

Example Question #21 : How To Solve Two Step Equations

Example Question #563 : Algebra 1

Example Question #563 : Linear Equations

Example Question #31 : How To Solve Two Step Equations

Example Question #565 : Linear Equations

Example Question #566 : Linear Equations

Example Question #32 : How To Solve Two Step Equations

Example Question #567 : Linear Equations

Example Question #568 : Linear Equations

All Algebra 1 Resources

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