Solve for x 4(x+2(3x-7))=22x-65

$4 (x + 2 (3 x - 7)) = 22 x - 65$

Step 1

Simplify $4 (x + 2 (3 x - 7))$ .

Rewrite.

$0 + 0 + 4 (x + 2 (3 x - 7)) = 22 x - 65$

Simplify by adding zeros.

$4 (x + 2 (3 x - 7)) = 22 x - 65$

Simplify each term.

Apply the distributive property.

$4 (x + 2 (3 x) + 2 \cdot - 7) = 22 x - 65$

Multiply $3$ by $2$ .

$4 (x + 6 x + 2 \cdot - 7) = 22 x - 65$

Multiply $2$ by $- 7$ .

$4 (x + 6 x - 14) = 22 x - 65$

Simplify terms.

Add $x$ and $6 x$ .

$4 (7 x - 14) = 22 x - 65$

Apply the distributive property.

$4 (7 x) + 4 \cdot - 14 = 22 x - 65$

Multiply.

Multiply $7$ by $4$ .

$28 x + 4 \cdot - 14 = 22 x - 65$

Multiply $4$ by $- 14$ .

$28 x - 56 = 22 x - 65$

Step 2

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

Subtract $22 x$ from both sides of the equation.

$28 x - 56 - 22 x = - 65$

Subtract $22 x$ from $28 x$ .

$6 x - 56 = - 65$

Step 3

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

Add $56$ to both sides of the equation.

$6 x = - 65 + 56$

Add $- 65$ and $56$ .

$6 x = - 9$

Step 4

Divide each term in $6 x = - 9$ by $6$ and simplify.

Divide each term in $6 x = - 9$ by $6$ .

$\frac{6 x}{6} = \frac{- 9}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 9}{6}$

Divide $x$ by $1$ .

$x = \frac{- 9}{6}$

Simplify the right side.

Cancel the common factor of $- 9$ and $6$ .

Factor $3$ out of $- 9$ .

$x = \frac{3 (- 3)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1.5$

Mixed Number Form:

$x = - 1 \frac{1}{2}$

Solve for x 4(x+2(3x-7))=22x-65

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