Solve for x (3x+7)/10+(3x+1)/8=x+7

$\frac{3 x + 7}{10} + \frac{3 x + 1}{8} = x + 7$

Step 1

Simplify $\frac{3 x + 7}{10} + \frac{3 x + 1}{8}$ .

To write $\frac{3 x + 7}{10}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x + 7}{10} \cdot \frac{4}{4} + \frac{3 x + 1}{8} = x + 7$

To write $\frac{3 x + 1}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x + 7}{10} \cdot \frac{4}{4} + \frac{3 x + 1}{8} \cdot \frac{5}{5} = x + 7$

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x + 7}{10}$ by $\frac{4}{4}$ .

$\frac{(3 x + 7) \cdot 4}{10 \cdot 4} + \frac{3 x + 1}{8} \cdot \frac{5}{5} = x + 7$

Multiply $10$ by $4$ .

$\frac{(3 x + 7) \cdot 4}{40} + \frac{3 x + 1}{8} \cdot \frac{5}{5} = x + 7$

Multiply $\frac{3 x + 1}{8}$ by $\frac{5}{5}$ .

$\frac{(3 x + 7) \cdot 4}{40} + \frac{(3 x + 1) \cdot 5}{8 \cdot 5} = x + 7$

Multiply $8$ by $5$ .

$\frac{(3 x + 7) \cdot 4}{40} + \frac{(3 x + 1) \cdot 5}{40} = x + 7$

Combine the numerators over the common denominator.

$\frac{(3 x + 7) \cdot 4 + (3 x + 1) \cdot 5}{40} = x + 7$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x \cdot 4 + 7 \cdot 4 + (3 x + 1) \cdot 5}{40} = x + 7$

Multiply $4$ by $3$ .

$\frac{12 x + 7 \cdot 4 + (3 x + 1) \cdot 5}{40} = x + 7$

Multiply $7$ by $4$ .

$\frac{12 x + 28 + (3 x + 1) \cdot 5}{40} = x + 7$

Apply the distributive property.

$\frac{12 x + 28 + 3 x \cdot 5 + 1 \cdot 5}{40} = x + 7$

Multiply $5$ by $3$ .

$\frac{12 x + 28 + 15 x + 1 \cdot 5}{40} = x + 7$

Multiply $5$ by $1$ .

$\frac{12 x + 28 + 15 x + 5}{40} = x + 7$

Add $12 x$ and $15 x$ .

$\frac{27 x + 28 + 5}{40} = x + 7$

Add $28$ and $5$ .

$\frac{27 x + 33}{40} = x + 7$

Factor $3$ out of $27 x + 33$ .

Factor $3$ out of $27 x$ .

$\frac{3 (9 x) + 33}{40} = x + 7$

Factor $3$ out of $33$ .

$\frac{3 (9 x) + 3 (11)}{40} = x + 7$

Factor $3$ out of $3 (9 x) + 3 (11)$ .

$\frac{3 (9 x + 11)}{40} = x + 7$

Step 2

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

Subtract $x$ from both sides of the equation.

$\frac{3 (9 x + 11)}{40} - x = 7$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{40}{40}$ .

$\frac{3 (9 x + 11)}{40} - x \cdot \frac{40}{40} = 7$

Combine $- x$ and $\frac{40}{40}$ .

$\frac{3 (9 x + 11)}{40} + \frac{- x \cdot 40}{40} = 7$

Combine the numerators over the common denominator.

$\frac{3 (9 x + 11) - x \cdot 40}{40} = 7$

Simplify the numerator.

Apply the distributive property.

$\frac{3 (9 x) + 3 \cdot 11 - x \cdot 40}{40} = 7$

Multiply $9$ by $3$ .

$\frac{27 x + 3 \cdot 11 - x \cdot 40}{40} = 7$

Multiply $3$ by $11$ .

$\frac{27 x + 33 - x \cdot 40}{40} = 7$

Multiply $40$ by $- 1$ .

$\frac{27 x + 33 - 40 x}{40} = 7$

Subtract $40 x$ from $27 x$ .

$\frac{- 13 x + 33}{40} = 7$

Factor $- 1$ out of $- 13 x$ .

$\frac{- (13 x) + 33}{40} = 7$

Rewrite $33$ as $- 1 (- 33)$ .

$\frac{- (13 x) - 1 (- 33)}{40} = 7$

Factor $- 1$ out of $- (13 x) - 1 (- 33)$ .

$\frac{- (13 x - 33)}{40} = 7$

Rewrite $- (13 x - 33)$ as $- 1 (13 x - 33)$ .

$\frac{- 1 (13 x - 33)}{40} = 7$

Move the negative in front of the fraction.

$- \frac{13 x - 33}{40} = 7$

Step 3

Multiply both sides of the equation by $- 40$ .

$- 40 (- \frac{13 x - 33}{40}) = - 40 \cdot 7$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 40 (- \frac{13 x - 33}{40})$ .

Cancel the common factor of $40$ .

Move the leading negative in $- \frac{13 x - 33}{40}$ into the numerator.

$- 40 \frac{- (13 x - 33)}{40} = - 40 \cdot 7$

Factor $40$ out of $- 40$ .

$40 (- 1) \frac{- (13 x - 33)}{40} = - 40 \cdot 7$

Cancel the common factor.

$40 \cdot - 1 \frac{- (13 x - 33)}{40} = - 40 \cdot 7$

Rewrite the expression.

$- - (13 x - 33) = - 40 \cdot 7$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (13 x - 33) = - 40 \cdot 7$

Multiply $13 x - 33$ by $1$ .

$13 x - 33 = - 40 \cdot 7$

Simplify the right side.

Multiply $- 40$ by $7$ .

$13 x - 33 = - 280$

Step 5

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

Add $33$ to both sides of the equation.

$13 x = - 280 + 33$

Add $- 280$ and $33$ .

$13 x = - 247$

Step 6

Divide each term in $13 x = - 247$ by $13$ and simplify.

Divide each term in $13 x = - 247$ by $13$ .

$\frac{13 x}{13} = \frac{- 247}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{- 247}{13}$

Divide $x$ by $1$ .

$x = \frac{- 247}{13}$

Simplify the right side.

Divide $- 247$ by $13$ .

$x = - 19$

Solve for x (3x+7)/10+(3x+1)/8=x+7

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