Solving a Linear Equation with Fractions
To solve the equation in the image, follow these steps:
\( \frac{3}{2} - (2x - 8) = 5 - 2(5x - 7) - 5 \)
First, distribute the negative sign through the parentheses on the left side:
\( \frac{3}{2} - 2x + 8 = 5 - 2(5x - 7) - 5 \)
Next, distribute the -2 on the right side:
\( \frac{3}{2} - 2x + 8 = 5 - 10x + 14 - 5 \)
Combine like terms on the right side:
\( \frac{3}{2} - 2x + 8 = 14 - 10x \)
Now, to get rid of the fraction on the left side, multiply every term in the equation by 2:
\( 2 * \frac{3}{2} - 2 * 2x + 2 * 8 = 2 * 14 - 2 * 10x \)
Simplify:
\( 3 - 4x + 16 = 28 - 20x \)
Now combine like terms on the left side:
\( 19 - 4x = 28 - 20x \)
Next, we want to get all the x terms on one side and constants on the other. Add 20x to both sides:
\( 19 - 4x + 20x = 28 - 20x + 20x \)
Simplify:
\( 19 + 16x = 28 \)
Subtract 19 from both sides to isolate the term with x:
\( 19 + 16x - 19 = 28 - 19 \)
Simplify:
\( 16x = 9 \)
Finally, divide by 16 to solve for x:
\( x = \frac{9}{16} \)
So the solution to the equation is \( x = \frac{9}{16} \).
