Solve for x 10+(2-x)/3=7

$10 + \frac{2 - x}{3} = 7$

Step 1

Simplify $10 + \frac{2 - x}{3}$ .

To write $10$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$10 \cdot \frac{3}{3} + \frac{2 - x}{3} = 7$

Simplify terms.

Combine $10$ and $\frac{3}{3}$ .

$\frac{10 \cdot 3}{3} + \frac{2 - x}{3} = 7$

Combine the numerators over the common denominator.

$\frac{10 \cdot 3 + 2 - x}{3} = 7$

Simplify the numerator.

Multiply $10$ by $3$ .

$\frac{30 + 2 - x}{3} = 7$

Add $30$ and $2$ .

$\frac{32 - x}{3} = 7$

Step 2

Multiply both sides by $3$ .

$\frac{32 - x}{3} \cdot 3 = 7 \cdot 3$

Step 3

Simplify.

Simplify the left side.

Simplify $\frac{32 - x}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{32 - x}{3} \cdot 3 = 7 \cdot 3$

Rewrite the expression.

$32 - x = 7 \cdot 3$

Reorder $32$ and $- x$ .

$- x + 32 = 7 \cdot 3$

Simplify the right side.

Multiply $7$ by $3$ .

$- x + 32 = 21$

Step 4

Solve for $x$ .

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

Subtract $32$ from both sides of the equation.

$- x = 21 - 32$

Subtract $32$ from $21$ .

$- x = - 11$

Divide each term in $- x = - 11$ by $- 1$ and simplify.

Divide each term in $- x = - 11$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 11}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 11}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 11}{- 1}$

Simplify the right side.

Divide $- 11$ by $- 1$ .

$x = 11$

Solve for x 10+(2-x)/3=7

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