### About Linear Equations in One Variable Part 2:

Now that we understand the four-step process for solving any linear equation in one variable, we turn to some special case scenarios. We learn how to clear an equation of fractions or decimals using our multiplication property of equality. We also learn about the three types of equations that we will encounter.

Test Objectives

- Demonstrate the ability to clear an equation of fractions
- Demonstrate the ability to clear an equation of decimals
- Demonstrate the ability to identify a special case linear equation

#1:

Instructions: Solve each equation.

a) -15 + 12x = -2(4 - 6x)

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#2:

Instructions: Solve each equation.

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

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#3:

Instructions: Solve each equation.

a) $$-\frac{31}{24}- x=-\frac{1}{3}\left(\frac{1}{2}x + \frac{3}{4}\right) $$

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#4:

Instructions: Solve each equation.

a) $$20 + 12n=4(3n + 5)$$

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#5:

Instructions: Solve each equation.

a) 7.18725 + 0.2x + 1.3 + 10x = 10.29x + 7.9

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Written Solutions:

#1:

Solutions:

a) no solution : ∅

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#2:

Solutions:

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

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#3:

Solutions:

a) $$x=-\frac{5}{4}$$

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#4:

Solutions:

a) {all real numbers}

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#5:

Solutions:

a) x = 6.525