Solve for a 1/3*(7a-1)=2a+7

$\frac{1}{3} \cdot (7 a - 1) = 2 a + 7$

Simplify $\frac{1}{3} \cdot (7 a - 1)$ .

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Apply the distributive property.

$\frac{1}{3} (7 a) + \frac{1}{3} \cdot - 1 = 2 a + 7$

Multiply $\frac{1}{3} (7 a)$ .

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Combine $7$ and $\frac{1}{3}$ .

$\frac{7}{3} a + \frac{1}{3} \cdot - 1 = 2 a + 7$

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

$\frac{7 a}{3} + \frac{1}{3} \cdot - 1 = 2 a + 7$

Combine $\frac{1}{3}$ and $- 1$ .

$\frac{7 a}{3} + \frac{- 1}{3} = 2 a + 7$

Move the negative in front of the fraction.

$\frac{7 a}{3} - \frac{1}{3} = 2 a + 7$

Move all terms containing $a$ to the left side of the equation.

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Subtract $2 a$ from both sides of the equation.

$\frac{7 a}{3} - \frac{1}{3} - 2 a = 7$

To write $- 2 a$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7 a}{3} - 2 a \cdot \frac{3}{3} - \frac{1}{3} = 7$

Combine $- 2 a$ and $\frac{3}{3}$ .

$\frac{7 a}{3} + \frac{- 2 a \cdot 3}{3} - \frac{1}{3} = 7$

Combine the numerators over the common denominator.

$\frac{7 a - 2 a \cdot 3}{3} - \frac{1}{3} = 7$

Combine the numerators over the common denominator.

$\frac{7 a - 2 a \cdot 3 - 1}{3} = 7$

Simplify the numerator.

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Multiply $3$ by $- 2$ .

$\frac{7 a - 6 a - 1}{3} = 7$

Subtract $6 a$ from $7 a$ .

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

Multiply both sides of the equation by $3$ .

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

Simplify both sides of the equation.

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Cancel the common factor of $3$ .

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Cancel the common factor.

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

Rewrite the expression.

$a - 1 = 3 \cdot 7$

Multiply $3$ by $7$ .

$a - 1 = 21$

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

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Add $1$ to both sides of the equation.

$a = 21 + 1$

Add $21$ and $1$ .

$a = 22$

Solve for a 1/3*(7a-1)=2a+7

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