Question

solve.
$\frac{x+1}{5}-\frac{1}{7}=\frac{x}{5}$

Explanation:

Step1: Write the given equation

$\frac{1}{5} - \frac{x+1}{7} = \frac{x}{5}$

Step2: Eliminate denominators (LCM=35)

Multiply each term by 35:
$35 \times \frac{1}{5} - 35 \times \frac{x+1}{7} = 35 \times \frac{x}{5}$
$7 - 5(x+1) = 7x$

Step3: Expand and simplify left side

$7 - 5x - 5 = 7x$
$2 - 5x = 7x$

Step4: Isolate x terms

Add $5x$ to both sides:
$2 = 7x + 5x$
$2 = 12x$

Step5: Solve for x

Divide by 12:
$x = \frac{2}{12} = \frac{1}{6}$

Answer:

$x = \frac{1}{6}$