### About Equations with Fractions:

When we encounter an equation with fractions, we have the choice to clear the fractions by multiplying both sides of the equation by the LCD of all fractions involved. Similarly, when we encounter decimals, we can clear them by multiplying both sides of the equation by the appropriate power of ten.

Test Objectives

- Demonstrate an understanding of how to solve a linear equation in one variable
- Demonstrate the ability to clear the fractions from an equation
- Demonstrate the ability to clear the decimals from an equation

#1:

Instructions: Solve each equation.

$$a)\hspace{.25em} \frac{-7x}{5} + 1 = \frac{-23}{15} + \frac{2x}{3} + \frac{2}{3} - \frac{1}{5}$$

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#2:

Instructions: Solve each equation.

$$a)\hspace{.25em}\frac{12}{5} + 2n = \frac{8n}{5} + \frac{7}{2} - 2$$

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#3:

Instructions: Solve each equation.

$$a)\hspace{.25em}\frac{25}{44} + 2x = \frac{-10}{11}\left(\frac{-1x}{2} + \frac{3}{2}\right)$$

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#4:

Instructions: Solve each equation.

a) -0.305x + 10.1805 = 1.3x + 3.6

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#5:

Instructions: Solve each equation.

a) -10.34 + 1 + 3.1x - 2.7x = -3.3x - 4.9

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Written Solutions:

#1:

Solutions:

a) x = 1

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#2:

Solutions:

$$a)\hspace{.25em}n = \frac{-9}{4}$$

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#3:

Solutions:

$$a)\hspace{.25em}n = \frac{-5}{4}$$

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#4:

Solutions:

a) x = 4.1

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#5:

Solutions:

a) x = 1.2