Finite Math Examples

$- \frac{7}{3} x + \frac{2}{3} = - 18$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{7}{3}$ .

$- \frac{x \cdot 7}{3} + \frac{2}{3} = - 18$

Step 1.2

Move $7$ to the left of $x$ .

$- \frac{7 x}{3} + \frac{2}{3} = - 18$

Step 2

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

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Step 2.1

Subtract $\frac{2}{3}$ from both sides of the equation.

$- \frac{7 x}{3} = - 18 - \frac{2}{3}$

Step 2.2

To write $- 18$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7 x}{3} = - 18 \cdot \frac{3}{3} - \frac{2}{3}$

Step 2.3

Combine $- 18$ and $\frac{3}{3}$ .

$- \frac{7 x}{3} = \frac{- 18 \cdot 3}{3} - \frac{2}{3}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{7 x}{3} = \frac{- 18 \cdot 3 - 2}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 18$ by $3$ .

$- \frac{7 x}{3} = \frac{- 54 - 2}{3}$

Step 2.5.2

Subtract $2$ from $- 54$ .

$- \frac{7 x}{3} = \frac{- 56}{3}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{7 x}{3} = - \frac{56}{3}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 7 x = - 56$

Step 4

Divide each term in $- 7 x = - 56$ by $- 7$ and simplify.

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Step 4.1

Divide each term in $- 7 x = - 56$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 56}{- 7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 56}{- 7}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 56}{- 7}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 56$ by $- 7$ .

$x = 8$