### About Equations with Fractions / Decimals:

Now that we understand the four-step process for solving any linear equation in one variable, we turn to some special case scenarios. We will practice clearing an equation of fractions or decimals using our multiplication property of equality.

Test Objectives
• Demonstrate the ability to solve a linear equation with fractions
• Demonstrate the ability to solve a linear equation with decimals
Solving Equations with Fractions / Decimals Practice Test:

#1:

Instructions: Solve each equation.

$$a)\hspace{.2em}{-}\frac{2}{3}x + \frac{11}{6}=x + \frac{91}{6}$$

$$b)\hspace{.2em}\frac{1}{4}x + \frac{15}{4}=\frac{15}{4}+ \frac{9}{7}x$$

#2:

Instructions: Solve each equation.

$$a)\hspace{.2em}{-}\frac{81}{14}+ \frac{1}{6}x=\frac{8}{7}x - \frac{23}{6}$$

$$b)\hspace{.2em}\frac{35}{12}x + 1 + \frac{1}{3}x=\frac{1}{2}x - \frac{1}{4}$$

#3:

Instructions: Solve each equation.

$$a)\hspace{.2em}\frac{207}{25}- \frac{7}{2}x=-\frac{9}{5}\left(\frac{3}{2}x - \frac{19}{5}\right)$$

$$b)\hspace{.2em}5.4x - 8.43=6.1x - 6.4$$

#4:

Instructions: Solve each equation.

$$a)\hspace{.2em}9.06 + 6x=3.4x - 2.9$$

$$b)\hspace{.2em}{-}5.5x + 6.1x=-3.7x - 13.76$$

#5:

Instructions: Solve each equation.

$$a)\hspace{.2em}7.68 - 3.3x=-4.9x - 4.8x$$

$$b)\hspace{.2em}{-}x + 15.6=-4.4(x - 3.7)$$

Written Solutions:

#1:

Solutions:

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

$$b)\hspace{.2em}x=0$$

#2:

Solutions:

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

$$b)\hspace{.2em}x=-\frac{5}{11}$$

#3:

Solutions:

$$a)\hspace{.2em}x=\frac{9}{5}$$

$$b)\hspace{.2em}x=-2.9$$

#4:

Solutions:

$$a)\hspace{.2em}x=-4.6$$

$$b)\hspace{.2em}x=-3.2$$

#5:

Solutions:

$$a)\hspace{.2em}x=-1.2$$

$$b)\hspace{.2em}x=0.2$$