About Solving Linear Equations:

In order to solve any linear equation in one variable, we must understand the four-step process. First, we collect terms and simplify each side. Then, we move all variable terms to one side and all numbers to the other. Next, we isolate the variable and finish our process by checking our result with substitution.


Test Objectives
  • Demonstrate an understanding of the addition property of equality
  • Demonstrate an understanding of the multiplication property of equality
  • Demonstrate the ability to solve any linear equation using the four-step procedure
Solving Linear Equations Practice Test:

#1:

Instructions: solve each equation.

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$$a)\hspace{.2em}11x + 5x=-3(x - 7) - 6(1 - 4x)$$

$$b)\hspace{.2em}10x + 2x=3(x - 10) - 7(5 - 2x)$$


#2:

Instructions: solve each equation.

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$$a)\hspace{.2em}-(2-10x)=8(x - 5)$$

$$b)\hspace{.2em}10(5x + 8) - 12x=-11(1 + 4x) + 9$$


#3:

Instructions: solve each equation.

$$a)\hspace{.2em}4(x - 5)=-2(x + 1)$$

$$b)\hspace{.2em}6(6 + 12x)=-1 + 7(10x + 7)$$


#4:

Instructions: solve each equation.

$$a)\hspace{.2em}10(4 + x)=2(5 + 2x)$$

$$b)\hspace{.2em}9(10 + 6x)=-12(1 - 3x) - 6$$


#5:

Instructions: solve each equation.

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$$a)\hspace{.2em}-11(10 + 7x) + 9x=7(1 - 11x)$$

$$b)\hspace{.2em}9x + 8(1 - 2x)=-5(x - 4)$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}x=-3$$

$$b)\hspace{.2em}x=13$$


#2:

Solutions:

$$a)\hspace{.2em}x=-19$$

$$b)\hspace{.2em}x=-1$$


#3:

Solutions:

$$a)\hspace{.2em}x=3$$

$$b)\hspace{.2em}x=6$$


#4:

Solutions:

$$a)\hspace{.2em}x=-5$$

$$b)\hspace{.2em}x=-6$$


#5:

Solutions:

$$a)\hspace{.2em}x=13$$

$$b)\hspace{.2em}x=-6$$