Solve for x 7(4x+1)-3x=5x-13

$7 (4 x + 1) - 3 x = 5 x - 13$

Step 1

Simplify $7 (4 x + 1) - 3 x$ .

Simplify each term.

Apply the distributive property.

$7 (4 x) + 7 \cdot 1 - 3 x = 5 x - 13$

Multiply $4$ by $7$ .

$28 x + 7 \cdot 1 - 3 x = 5 x - 13$

Multiply $7$ by $1$ .

$28 x + 7 - 3 x = 5 x - 13$

Subtract $3 x$ from $28 x$ .

$25 x + 7 = 5 x - 13$

Step 2

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

Subtract $5 x$ from both sides of the equation.

$25 x + 7 - 5 x = - 13$

Subtract $5 x$ from $25 x$ .

$20 x + 7 = - 13$

Step 3

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

Subtract $7$ from both sides of the equation.

$20 x = - 13 - 7$

Subtract $7$ from $- 13$ .

$20 x = - 20$

Step 4

Divide each term in $20 x = - 20$ by $20$ and simplify.

Divide each term in $20 x = - 20$ by $20$ .

$\frac{20 x}{20} = \frac{- 20}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 x}{20} = \frac{- 20}{20}$

Divide $x$ by $1$ .

$x = \frac{- 20}{20}$

Simplify the right side.

Divide $- 20$ by $20$ .

$x = - 1$