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

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

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.

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

Step 2

Simplify $9 (1 + x) - 5 x$ .

Simplify each term.

Apply the distributive property.

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

Multiply $9$ by $1$ .

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

Subtract $5 x$ from $9 x$ .

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

Step 3

Simplify $2 (2 x - 1) + 10$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $2$ .

$9 + 4 x = 4 x + 2 \cdot - 1 + 10$

Multiply $2$ by $- 1$ .

$9 + 4 x = 4 x - 2 + 10$

Add $- 2$ and $10$ .

$9 + 4 x = 4 x + 8$

Step 4

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

Subtract $4 x$ from both sides of the equation.

$9 + 4 x - 4 x = 8$

Combine the opposite terms in $9 + 4 x - 4 x$ .

Subtract $4 x$ from $4 x$ .

$9 + 0 = 8$

Add $9$ and $0$ .

$9 = 8$

Step 5

Since $9 \neq 8$ , there are no solutions.

No solution