Question - Solving a Linear Equation with Fractions
Solution:
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 $$ x = \frac{9}{16} $$.
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