Solve for x -5/4x=-x+3(-1/3x+1)+1

$- \frac{5}{4} x = - x + 3 (- \frac{1}{3} x + 1) + 1$

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.

$- x + 3 (- \frac{1}{3} x + 1) + 1 = - \frac{5}{4} x$

Step 2

Simplify $- x + 3 (- \frac{1}{3} x + 1) + 1$ .

Simplify each term.

Combine $x$ and $\frac{1}{3}$ .

$- x + 3 (- \frac{x}{3} + 1) + 1 = - \frac{5}{4} x$

Apply the distributive property.

$- x + 3 (- \frac{x}{3}) + 3 \cdot 1 + 1 = - \frac{5}{4} x$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- x + 3 \frac{- x}{3} + 3 \cdot 1 + 1 = - \frac{5}{4} x$

Cancel the common factor.

$- x + 3 \frac{- x}{3} + 3 \cdot 1 + 1 = - \frac{5}{4} x$

Rewrite the expression.

$- x - x + 3 \cdot 1 + 1 = - \frac{5}{4} x$

Multiply $3$ by $1$ .

$- x - x + 3 + 1 = - \frac{5}{4} x$

Simplify by adding terms.

Subtract $x$ from $- x$ .

$- 2 x + 3 + 1 = - \frac{5}{4} x$

Add $3$ and $1$ .

$- 2 x + 4 = - \frac{5}{4} x$

Step 3

Simplify $- \frac{5}{4} x$ .

Combine $x$ and $\frac{5}{4}$ .

$- 2 x + 4 = - \frac{x \cdot 5}{4}$

Move $5$ to the left of $x$ .

$- 2 x + 4 = - \frac{5 x}{4}$

Step 4

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

Add $\frac{5 x}{4}$ to both sides of the equation.

$- 2 x + 4 + \frac{5 x}{4} = 0$

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 2 x \cdot \frac{4}{4} + \frac{5 x}{4} + 4 = 0$

Combine $- 2 x$ and $\frac{4}{4}$ .

$\frac{- 2 x \cdot 4}{4} + \frac{5 x}{4} + 4 = 0$

Combine the numerators over the common denominator.

$\frac{- 2 x \cdot 4 + 5 x}{4} + 4 = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 2 x \cdot 4 + 5 x$ .

Factor $x$ out of $- 2 x \cdot 4$ .

$\frac{x (- 2 \cdot 4) + 5 x}{4} + 4 = 0$

Factor $x$ out of $5 x$ .

$\frac{x (- 2 \cdot 4) + x \cdot 5}{4} + 4 = 0$

Factor $x$ out of $x (- 2 \cdot 4) + x \cdot 5$ .

$\frac{x (- 2 \cdot 4 + 5)}{4} + 4 = 0$

Multiply $- 2$ by $4$ .

$\frac{x (- 8 + 5)}{4} + 4 = 0$

Add $- 8$ and $5$ .

$\frac{x \cdot - 3}{4} + 4 = 0$

Move $- 3$ to the left of $x$ .

$\frac{- 3 \cdot x}{4} + 4 = 0$

Move the negative in front of the fraction.

$- \frac{3 x}{4} + 4 = 0$

Step 5

Subtract $4$ from both sides of the equation.

$- \frac{3 x}{4} = - 4$

Step 6

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} \cdot - 4$

Step 7

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{3} (- \frac{3 x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} \cdot - 4$

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 4$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 4$

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 4$

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{4}{3} \cdot - 4$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} \cdot - 4$

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} \cdot - 4$

Rewrite the expression.

$- - x = - \frac{4}{3} \cdot - 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{3} \cdot - 4$

Multiply $x$ by $1$ .

$x = - \frac{4}{3} \cdot - 4$

Simplify the right side.

Multiply $- \frac{4}{3} \cdot - 4$ .

Multiply $- 4$ by $- 1$ .

$x = 4 (\frac{4}{3})$

Combine $4$ and $\frac{4}{3}$ .

$x = \frac{4 \cdot 4}{3}$

Multiply $4$ by $4$ .

$x = \frac{16}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{16}{3}$

Decimal Form:

$x = 5.\overline{3}$

Mixed Number Form:

$x = 5 \frac{1}{3}$

Solve for x -5/4x=-x+3(-1/3x+1)+1

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