Solve for x 9(2-3x)-29=8x-(x-23)

$9 (2 - 3 x) - 29 = 8 x - (x - 23)$

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.

$8 x - (x - 23) = 9 (2 - 3 x) - 29$

Step 2

Simplify $8 x - (x - 23)$ .

Simplify each term.

Apply the distributive property.

$8 x - x - - 23 = 9 (2 - 3 x) - 29$

Multiply $- 1$ by $- 23$ .

$8 x - x + 23 = 9 (2 - 3 x) - 29$

Subtract $x$ from $8 x$ .

$7 x + 23 = 9 (2 - 3 x) - 29$

Step 3

Simplify $9 (2 - 3 x) - 29$ .

Simplify each term.

Apply the distributive property.

$7 x + 23 = 9 \cdot 2 + 9 (- 3 x) - 29$

Multiply $9$ by $2$ .

$7 x + 23 = 18 + 9 (- 3 x) - 29$

Multiply $- 3$ by $9$ .

$7 x + 23 = 18 - 27 x - 29$

Subtract $29$ from $18$ .

$7 x + 23 = - 27 x - 11$

Step 4

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

Add $27 x$ to both sides of the equation.

$7 x + 23 + 27 x = - 11$

Add $7 x$ and $27 x$ .

$34 x + 23 = - 11$

Step 5

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

Subtract $23$ from both sides of the equation.

$34 x = - 11 - 23$

Subtract $23$ from $- 11$ .

$34 x = - 34$

Step 6

Divide each term in $34 x = - 34$ by $34$ and simplify.

Divide each term in $34 x = - 34$ by $34$ .

$\frac{34 x}{34} = \frac{- 34}{34}$

Simplify the left side.

Cancel the common factor of $34$ .

Cancel the common factor.

$\frac{34 x}{34} = \frac{- 34}{34}$

Divide $x$ by $1$ .

$x = \frac{- 34}{34}$

Simplify the right side.

Divide $- 34$ by $34$ .

$x = - 1$

Solve for x 9(2-3x)-29=8x-(x-23)

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