Ask a New Question
Menu

Solve the equation.

StartFraction 5 left parenthesis x minus 2 right parenthesis Over 6 EndFraction minus x equals 1 minus StartFraction x Over 8 EndFraction
Question content area bottom
Part 1
xequals
  
enter your response here
​(Simplify your​ answer.)

1 answer

To solve the equation

\[ \frac{5(x - 2)}{6} - x = 1 - \frac{x}{8}, \]

let's start by eliminating the fractions. We can do this by finding the least common multiple of the denominators. The denominators are 6 and 8, and the least common multiple (LCM) is 24. We will multiply each term of the equation by 24.

  1. Multiply through by 24:

\[ 24 \left(\frac{5(x - 2)}{6}\right) - 24(x) = 24\left(1\right) - 24\left(\frac{x}{8}\right). \]

  1. Simplifying each term, we get:

\[ 4 \cdot 5(x - 2) - 24x = 24 - 3x. \]

This simplifies to:

\[ 20(x - 2) - 24x = 24 - 3x. \]

  1. Distributing the 20:

\[ 20x - 40 - 24x = 24 - 3x. \]

  1. Combine like terms on the left side:

\[ (20x - 24x) - 40 = 24 - 3x, \] which simplifies to: \[ -4x - 40 = 24 - 3x. \]

  1. To isolate x, first add 3x to both sides:

\[ -4x + 3x - 40 = 24, \]

which simplifies to:

\[ -x - 40 = 24. \]

  1. Now add 40 to both sides:

\[ -x = 64. \]

  1. Finally, multiply by -1:

\[ x = -64. \]

Thus, the solution is

\[ \boxed{-64}. \]