Finite Math Examples

$56 - \frac{4}{3} x = 48 - x$

Step 1

Simplify each term.

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Step 1.1

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

$56 - \frac{x \cdot 4}{3} = 48 - x$

Step 1.2

Move $4$ to the left of $x$ .

$56 - \frac{4 x}{3} = 48 - x$

Step 2

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

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Step 2.1

Add $x$ to both sides of the equation.

$56 - \frac{4 x}{3} + x = 48$

Step 2.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$56 - \frac{4 x}{3} + x \cdot \frac{3}{3} = 48$

Step 2.3

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

$56 - \frac{4 x}{3} + \frac{x \cdot 3}{3} = 48$

Step 2.4

Combine the numerators over the common denominator.

$56 + \frac{- 4 x + x \cdot 3}{3} = 48$

Step 2.5

Add $- 4 x$ and $x \cdot 3$ .

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Step 2.5.1

Reorder $x$ and $3$ .

$56 + \frac{- 4 x + 3 \cdot x}{3} = 48$

Step 2.5.2

Add $- 4 x$ and $3 \cdot x$ .

$56 + \frac{- x}{3} = 48$

Step 2.6

Move the negative in front of the fraction.

$56 - \frac{x}{3} = 48$

Step 3

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

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Step 3.1

Subtract $56$ from both sides of the equation.

$- \frac{x}{3} = 48 - 56$

Step 3.2

Subtract $56$ from $48$ .

$- \frac{x}{3} = - 8$

Step 4

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{x}{3}) = - 3 \cdot - 8$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

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

$- 3 \frac{- x}{3} = - 3 \cdot - 8$

Step 5.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- x}{3} = - 3 \cdot - 8$

Step 5.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} = - 3 \cdot - 8$

Step 5.1.1.1.4

Rewrite the expression.

$- - x = - 3 \cdot - 8$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 3 \cdot - 8$

Step 5.1.1.2.2

Multiply $x$ by $1$ .

$x = - 3 \cdot - 8$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 3$ by $- 8$ .

$x = 24$