Solve for x 2(4x-9)=5(x-4)

$2 (4 x - 9) = 5 (x - 4)$

Step 1

Simplify $2 (4 x - 9)$ .

Rewrite.

$0 + 0 + 2 (4 x - 9) = 5 (x - 4)$

Simplify by adding zeros.

$2 (4 x - 9) = 5 (x - 4)$

Apply the distributive property.

$2 (4 x) + 2 \cdot - 9 = 5 (x - 4)$

Multiply.

Multiply $4$ by $2$ .

$8 x + 2 \cdot - 9 = 5 (x - 4)$

Multiply $2$ by $- 9$ .

$8 x - 18 = 5 (x - 4)$

Step 2

Simplify $5 (x - 4)$ .

Apply the distributive property.

$8 x - 18 = 5 x + 5 \cdot - 4$

Multiply $5$ by $- 4$ .

$8 x - 18 = 5 x - 20$

Step 3

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

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

$8 x - 18 - 5 x = - 20$

Subtract $5 x$ from $8 x$ .

$3 x - 18 = - 20$

Step 4

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

Add $18$ to both sides of the equation.

$3 x = - 20 + 18$

Add $- 20$ and $18$ .

$3 x = - 2$

Step 5

Divide each term in $3 x = - 2$ by $3$ and simplify.

Divide each term in $3 x = - 2$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.\overline{6}$

Solve for x 2(4x-9)=5(x-4)

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