Solve for x 3/7x+3-x+3=2

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

Step 1

Simplify $\frac{3}{7} x + 3 - x + 3$ .

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

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

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

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

Combine $- x$ and $\frac{7}{7}$ .

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

Combine the numerators over the common denominator.

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

Find the common denominator.

Write $3$ as a fraction with denominator $1$ .

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

Multiply $\frac{3}{1}$ by $\frac{7}{7}$ .

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

Multiply $\frac{3}{1}$ by $\frac{7}{7}$ .

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

Write $3$ as a fraction with denominator $1$ .

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

Multiply $\frac{3}{1}$ by $\frac{7}{7}$ .

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

Multiply $\frac{3}{1}$ by $\frac{7}{7}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Multiply $7$ by $- 1$ .

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

Multiply $3$ by $7$ .

$\frac{3 x - 7 x + 21 + 3 \cdot 7}{7} = 2$

Multiply $3$ by $7$ .

$\frac{3 x - 7 x + 21 + 21}{7} = 2$

Simplify terms.

Subtract $7 x$ from $3 x$ .

$\frac{- 4 x + 21 + 21}{7} = 2$

Add $21$ and $21$ .

$\frac{- 4 x + 42}{7} = 2$

Factor $2$ out of $- 4 x + 42$ .

Factor $2$ out of $- 4 x$ .

$\frac{2 (- 2 x) + 42}{7} = 2$

Factor $2$ out of $42$ .

$\frac{2 (- 2 x) + 2 (21)}{7} = 2$

Factor $2$ out of $2 (- 2 x) + 2 (21)$ .

$\frac{2 (- 2 x + 21)}{7} = 2$

Factor $- 1$ out of $- 2 x$ .

$\frac{2 (- (2 x) + 21)}{7} = 2$

Rewrite $21$ as $- 1 (- 21)$ .

$\frac{2 (- (2 x) - 1 (- 21))}{7} = 2$

Factor $- 1$ out of $- (2 x) - 1 (- 21)$ .

$\frac{2 (- (2 x - 21))}{7} = 2$

Simplify the expression.

Rewrite $- (2 x - 21)$ as $- 1 (2 x - 21)$ .

$\frac{2 (- 1 (2 x - 21))}{7} = 2$

Move the negative in front of the fraction.

$- \frac{2 (2 x - 21)}{7} = 2$

Step 2

Multiply both sides of the equation by $- \frac{7}{2}$ .

$- \frac{7}{2} (- \frac{2 (2 x - 21)}{7}) = - \frac{7}{2} \cdot 2$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{7}{2} (- \frac{2 (2 x - 21)}{7})$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$\frac{- 7}{2} (- \frac{2 (2 x - 21)}{7}) = - \frac{7}{2} \cdot 2$

Move the leading negative in $- \frac{2 (2 x - 21)}{7}$ into the numerator.

$\frac{- 7}{2} \cdot \frac{- 2 (2 x - 21)}{7} = - \frac{7}{2} \cdot 2$

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{2} \cdot \frac{- 2 (2 x - 21)}{7} = - \frac{7}{2} \cdot 2$

Cancel the common factor.

$\frac{7 \cdot - 1}{2} \cdot \frac{- 2 (2 x - 21)}{7} = - \frac{7}{2} \cdot 2$

Rewrite the expression.

$\frac{- 1}{2} (- 2 (2 x - 21)) = - \frac{7}{2} \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 (2 x - 21)$ .

$\frac{- 1}{2} (2 (- (2 x - 21))) = - \frac{7}{2} \cdot 2$

Cancel the common factor.

$\frac{- 1}{2} (2 (- (2 x - 21))) = - \frac{7}{2} \cdot 2$

Rewrite the expression.

$- - (2 x - 21) = - \frac{7}{2} \cdot 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (2 x - 21) = - \frac{7}{2} \cdot 2$

Multiply $2 x - 21$ by $1$ .

$2 x - 21 = - \frac{7}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$2 x - 21 = \frac{- 7}{2} \cdot 2$

Cancel the common factor.

$2 x - 21 = \frac{- 7}{2} \cdot 2$

Rewrite the expression.

$2 x - 21 = - 7$

Step 4

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

Add $21$ to both sides of the equation.

$2 x = - 7 + 21$

Add $- 7$ and $21$ .

$2 x = 14$

Step 5

Divide each term in $2 x = 14$ by $2$ and simplify.

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x = 7$

Solve for x 3/7x+3-x+3=2

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