Solve for x 10(x-9)-9(5-6x)=2(4x-1)+5(1+2x)

$10 (x - 9) - 9 (5 - 6 x) = 2 (4 x - 1) + 5 (1 + 2 x)$

Step 1

Simplify $10 (x - 9) - 9 (5 - 6 x)$ .

Simplify each term.

Apply the distributive property.

$10 x + 10 \cdot - 9 - 9 (5 - 6 x) = 2 (4 x - 1) + 5 (1 + 2 x)$

Multiply $10$ by $- 9$ .

$10 x - 90 - 9 (5 - 6 x) = 2 (4 x - 1) + 5 (1 + 2 x)$

Apply the distributive property.

$10 x - 90 - 9 \cdot 5 - 9 (- 6 x) = 2 (4 x - 1) + 5 (1 + 2 x)$

Multiply $- 9$ by $5$ .

$10 x - 90 - 45 - 9 (- 6 x) = 2 (4 x - 1) + 5 (1 + 2 x)$

Multiply $- 6$ by $- 9$ .

$10 x - 90 - 45 + 54 x = 2 (4 x - 1) + 5 (1 + 2 x)$

Simplify by adding terms.

Add $10 x$ and $54 x$ .

$64 x - 90 - 45 = 2 (4 x - 1) + 5 (1 + 2 x)$

Subtract $45$ from $- 90$ .

$64 x - 135 = 2 (4 x - 1) + 5 (1 + 2 x)$

Step 2

Simplify $2 (4 x - 1) + 5 (1 + 2 x)$ .

Simplify each term.

Apply the distributive property.

$64 x - 135 = 2 (4 x) + 2 \cdot - 1 + 5 (1 + 2 x)$

Multiply $4$ by $2$ .

$64 x - 135 = 8 x + 2 \cdot - 1 + 5 (1 + 2 x)$

Multiply $2$ by $- 1$ .

$64 x - 135 = 8 x - 2 + 5 (1 + 2 x)$

Apply the distributive property.

$64 x - 135 = 8 x - 2 + 5 \cdot 1 + 5 (2 x)$

Multiply $5$ by $1$ .

$64 x - 135 = 8 x - 2 + 5 + 5 (2 x)$

Multiply $2$ by $5$ .

$64 x - 135 = 8 x - 2 + 5 + 10 x$

Simplify by adding terms.

Add $8 x$ and $10 x$ .

$64 x - 135 = 18 x - 2 + 5$

Add $- 2$ and $5$ .

$64 x - 135 = 18 x + 3$

Step 3

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

Subtract $18 x$ from both sides of the equation.

$64 x - 135 - 18 x = 3$

Subtract $18 x$ from $64 x$ .

$46 x - 135 = 3$

Step 4

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

Add $135$ to both sides of the equation.

$46 x = 3 + 135$

Add $3$ and $135$ .

$46 x = 138$

Step 5

Divide each term in $46 x = 138$ by $46$ and simplify.

Divide each term in $46 x = 138$ by $46$ .

$\frac{46 x}{46} = \frac{138}{46}$

Simplify the left side.

Cancel the common factor of $46$ .

Cancel the common factor.

$\frac{46 x}{46} = \frac{138}{46}$

Divide $x$ by $1$ .

$x = \frac{138}{46}$

Simplify the right side.

Divide $138$ by $46$ .

$x = 3$

Solve for x 10(x-9)-9(5-6x)=2(4x-1)+5(1+2x)

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