Solve for a 5/7a+1/7=3

$\frac{5}{7} a + \frac{1}{7} = 3$

Step 1

Combine $\frac{5}{7}$ and $a$ .

$\frac{5 a}{7} + \frac{1}{7} = 3$

Step 2

Move all terms not containing $a$ to the right side of the equation.

Subtract $\frac{1}{7}$ from both sides of the equation.

$\frac{5 a}{7} = 3 - \frac{1}{7}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{5 a}{7} = 3 \cdot \frac{7}{7} - \frac{1}{7}$

Combine $3$ and $\frac{7}{7}$ .

$\frac{5 a}{7} = \frac{3 \cdot 7}{7} - \frac{1}{7}$

Combine the numerators over the common denominator.

$\frac{5 a}{7} = \frac{3 \cdot 7 - 1}{7}$

Simplify the numerator.

Multiply $3$ by $7$ .

$\frac{5 a}{7} = \frac{21 - 1}{7}$

Subtract $1$ from $21$ .

$\frac{5 a}{7} = \frac{20}{7}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$5 a = 20$

Step 4

Divide each term in $5 a = 20$ by $5$ and simplify.

Divide each term in $5 a = 20$ by $5$ .

$\frac{5 a}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 a}{5} = \frac{20}{5}$

Divide $a$ by $1$ .

$a = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$a = 4$