Solve for x 3(4x+3)=2x-5(3-x)+2

$3 (4 x + 3) = 2 x - 5 (3 - x) + 2$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 x - 5 (3 - x) + 2 = 3 (4 x + 3)$

Step 2

Simplify $2 x - 5 (3 - x) + 2$ .

Simplify each term.

Apply the distributive property.

$2 x - 5 \cdot 3 - 5 (- x) + 2 = 3 (4 x + 3)$

Multiply $- 5$ by $3$ .

$2 x - 15 - 5 (- x) + 2 = 3 (4 x + 3)$

Multiply $- 1$ by $- 5$ .

$2 x - 15 + 5 x + 2 = 3 (4 x + 3)$

Simplify by adding terms.

Add $2 x$ and $5 x$ .

$7 x - 15 + 2 = 3 (4 x + 3)$

Add $- 15$ and $2$ .

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

Step 3

Simplify $3 (4 x + 3)$ .

Apply the distributive property.

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

Multiply.

Multiply $4$ by $3$ .

$7 x - 13 = 12 x + 3 \cdot 3$

Multiply $3$ by $3$ .

$7 x - 13 = 12 x + 9$

Step 4

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

Subtract $12 x$ from both sides of the equation.

$7 x - 13 - 12 x = 9$

Subtract $12 x$ from $7 x$ .

$- 5 x - 13 = 9$

Step 5

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

Add $13$ to both sides of the equation.

$- 5 x = 9 + 13$

Add $9$ and $13$ .

$- 5 x = 22$

Step 6

Divide each term in $- 5 x = 22$ by $- 5$ and simplify.

Divide each term in $- 5 x = 22$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{22}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{22}{- 5}$

Divide $x$ by $1$ .

$x = \frac{22}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{22}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{22}{5}$

Decimal Form:

$x = - 4.4$

Mixed Number Form:

$x = - 4 \frac{2}{5}$

Solve for x 3(4x+3)=2x-5(3-x)+2

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