Question

solve the following equation.
$\frac{x}{7} - \frac{7}{5} = \frac{5x + 49}{7}$

Explanation:

Step1: Simplify left side

$\frac{x}{7} - \frac{7}{5} = \frac{5x - 49}{35}$

Step2: Set equal to right side

$\frac{5x - 49}{35} = \frac{5x + 49}{7}$

Step3: Cross-multiply to eliminate denominators

$7(5x - 49) = 35(5x + 49)$

Step4: Simplify both sides

$35x - 343 = 175x + 1715$

Step5: Isolate x terms

$35x - 175x = 1715 + 343$

Step6: Calculate and solve for x

$-140x = 2058$
$x = \frac{2058}{-140} = -\frac{147}{10}$

Answer:

$x = -\frac{147}{10}$ or $x = -14.7$