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Question:
What is the solution to the linear equation?
[tex]x - \frac{2}{3}x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6}x[/tex]
Answer:
[tex]x = \frac{-5}{3}[/tex]
Step-by-step explanation:
Given
[tex]x - \frac{2}{3}x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6}x[/tex]
Required
Simplify
[tex]x - \frac{2}{3}x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6}x[/tex]
Add [tex]\frac{1}{2}[/tex] to both sides
[tex]x - \frac{2}{3}x - \frac{1}{2} + \frac{1}{2} = \frac{1}{3} + \frac{5}{6}x + \frac{1}{2}[/tex]
[tex]x - \frac{2}{3}x = \frac{1}{3} + \frac{5}{6}x + \frac{1}{2}[/tex]
Subtract [tex]\frac{5}{6}x[/tex] from both sides
[tex]x - \frac{2}{3}x - \frac{5}{6}x= \frac{1}{3} + \frac{5}{6}x + \frac{1}{2} - \frac{5}{6}x[/tex]
[tex]x - \frac{2}{3}x - \frac{5}{6}x= \frac{1}{3} + \frac{1}{2} + \frac{5}{6}x- \frac{5}{6}x[/tex]
[tex]x - \frac{2}{3}x - \frac{5}{6}x= \frac{1}{3} + \frac{1}{2}[/tex]
Take LCMs
[tex]\frac{6x - 4x -5x}{6}= \frac{2+3}{6}[/tex]
[tex]\frac{-3x}{6}= \frac{5}{6}[/tex]
Multiply both sides by 6
[tex]6 * \frac{-3x}{6}= \frac{5}{6} * 6[/tex]
[tex]-3x= 5[/tex]
Divide both sides by -3
[tex]\frac{-3x}{-3}= \frac{5}{-3}[/tex]
[tex]x = \frac{5}{-3}[/tex]
[tex]x = \frac{-5}{3}[/tex]
