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

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

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.

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

Step 2

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

Simplify each term.

Apply the distributive property.

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

Multiply $- 5$ by $1$ .

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

Multiply $- 4$ by $- 5$ .

$2 x + 2 - 5 + 20 x = 4 (2 - x) + 1$

Simplify by adding terms.

Add $2 x$ and $20 x$ .

$22 x + 2 - 5 = 4 (2 - x) + 1$

Subtract $5$ from $2$ .

$22 x - 3 = 4 (2 - x) + 1$

Step 3

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

Simplify each term.

Apply the distributive property.

$22 x - 3 = 4 \cdot 2 + 4 (- x) + 1$

Multiply $4$ by $2$ .

$22 x - 3 = 8 + 4 (- x) + 1$

Multiply $- 1$ by $4$ .

$22 x - 3 = 8 - 4 x + 1$

Add $8$ and $1$ .

$22 x - 3 = - 4 x + 9$

Step 4

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

Add $4 x$ to both sides of the equation.

$22 x - 3 + 4 x = 9$

Add $22 x$ and $4 x$ .

$26 x - 3 = 9$

Step 5

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

Add $3$ to both sides of the equation.

$26 x = 9 + 3$

Add $9$ and $3$ .

$26 x = 12$

Step 6

Divide each term in $26 x = 12$ by $26$ and simplify.

Divide each term in $26 x = 12$ by $26$ .

$\frac{26 x}{26} = \frac{12}{26}$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 x}{26} = \frac{12}{26}$

Divide $x$ by $1$ .

$x = \frac{12}{26}$

Simplify the right side.

Cancel the common factor of $12$ and $26$ .

Factor $2$ out of $12$ .

$x = \frac{2 (6)}{26}$

Cancel the common factors.

Factor $2$ out of $26$ .

$x = \frac{2 \cdot 6}{2 \cdot 13}$

Cancel the common factor.

$x = \frac{2 \cdot 6}{2 \cdot 13}$

Rewrite the expression.

$x = \frac{6}{13}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{13}$

Decimal Form:

$x = 0.\overline{461538}$

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

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