Solve for x (2x+8)/21+(x+1)/3=-7

$\frac{2 x + 8}{21} + \frac{x + 1}{3} = - 7$

Simplify $\frac{2 x + 8}{21} + \frac{x + 1}{3}$ .

Factor $2$ out of $2 x + 8$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 8}{21} + \frac{x + 1}{3} = - 7$

Factor $2$ out of $8$ .

$\frac{2 x + 2 \cdot 4}{21} + \frac{x + 1}{3} = - 7$

Factor $2$ out of $2 x + 2 \cdot 4$ .

$\frac{2 (x + 4)}{21} + \frac{x + 1}{3} = - 7$

To write $\frac{x + 1}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2 (x + 4)}{21} + \frac{x + 1}{3} \cdot \frac{7}{7} = - 7$

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{2 (x + 4)}{21} + \frac{(x + 1) \cdot 7}{3 \cdot 7} = - 7$

Multiply $3$ by $7$ .

$\frac{2 (x + 4)}{21} + \frac{(x + 1) \cdot 7}{21} = - 7$

Combine the numerators over the common denominator.

$\frac{2 (x + 4) + (x + 1) \cdot 7}{21} = - 7$

Simplify the numerator.

Apply the distributive property.

$\frac{2 x + 2 \cdot 4 + (x + 1) \cdot 7}{21} = - 7$

Multiply $2$ by $4$ .

$\frac{2 x + 8 + (x + 1) \cdot 7}{21} = - 7$

Apply the distributive property.

$\frac{2 x + 8 + x \cdot 7 + 1 \cdot 7}{21} = - 7$

Move $7$ to the left of $x$ .

$\frac{2 x + 8 + 7 \cdot x + 1 \cdot 7}{21} = - 7$

Multiply $7$ by $1$ .

$\frac{2 x + 8 + 7 \cdot x + 7}{21} = - 7$

Add $2 x$ and $7 x$ .

$\frac{9 x + 8 + 7}{21} = - 7$

Add $8$ and $7$ .

$\frac{9 x + 15}{21} = - 7$

Factor $3$ out of $9 x + 15$ .

Factor $3$ out of $9 x$ .

$\frac{3 (3 x) + 15}{21} = - 7$

Factor $3$ out of $15$ .

$\frac{3 (3 x) + 3 (5)}{21} = - 7$

Factor $3$ out of $3 (3 x) + 3 (5)$ .

$\frac{3 (3 x + 5)}{21} = - 7$

Cancel the common factors.

Factor $3$ out of $21$ .

$\frac{3 (3 x + 5)}{3 \cdot 7} = - 7$

Cancel the common factor.

$\frac{3 (3 x + 5)}{3 \cdot 7} = - 7$

Rewrite the expression.

$\frac{3 x + 5}{7} = - 7$

Multiply both sides by $7$ .

$\frac{3 x + 5}{7} \cdot 7 = - 7 \cdot 7$

Simplify.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{3 x + 5}{7} \cdot 7 = - 7 \cdot 7$

Rewrite the expression.

$3 x + 5 = - 7 \cdot 7$

Simplify the right side.

Multiply $- 7$ by $7$ .

$3 x + 5 = - 49$

Solve for $x$ .

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

Subtract $5$ from both sides of the equation.

$3 x = - 49 - 5$

Subtract $5$ from $- 49$ .

$3 x = - 54$

Divide each term in $3 x = - 54$ by $3$ and simplify.

Divide each term in $3 x = - 54$ by $3$ .

$\frac{3 x}{3} = \frac{- 54}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 54}{3}$

Divide $x$ by $1$ .

$x = \frac{- 54}{3}$

Simplify the right side.

Divide $- 54$ by $3$ .

$x = - 18$

Solve for x (2x+8)/21+(x+1)/3=-7

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