Algebra Examples

$x + 7 - 8 \frac{x}{3} = \frac{17}{6} - 5 \frac{x}{2}$

Step 1

Simplify $x + 7 - 8 \frac{x}{3}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $- 8$ and $\frac{x}{3}$ .

$x + 7 + \frac{- 8 x}{3} = \frac{17}{6} - 5 \frac{x}{2}$

Step 1.1.2

Move the negative in front of the fraction.

$x + 7 - \frac{8 x}{3} = \frac{17}{6} - 5 \frac{x}{2}$

Step 1.2

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

$x \cdot \frac{3}{3} - \frac{8 x}{3} + 7 = \frac{17}{6} - 5 \frac{x}{2}$

Step 1.3

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

$\frac{x \cdot 3}{3} - \frac{8 x}{3} + 7 = \frac{17}{6} - 5 \frac{x}{2}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - 8 x}{3} + 7 = \frac{17}{6} - 5 \frac{x}{2}$

Step 1.5

Subtract $8 x$ from $x \cdot 3$ .

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Step 1.5.1

Reorder $x$ and $3$ .

$\frac{3 \cdot x - 8 x}{3} + 7 = \frac{17}{6} - 5 \frac{x}{2}$

Step 1.5.2

Subtract $8 x$ from $3 \cdot x$ .

$\frac{- 5 \cdot x}{3} + 7 = \frac{17}{6} - 5 \frac{x}{2}$

Step 1.6

Move the negative in front of the fraction.

$- \frac{5 x}{3} + 7 = \frac{17}{6} - 5 \frac{x}{2}$

Step 2

Simplify each term.

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Step 2.1

Combine $- 5$ and $\frac{x}{2}$ .

$- \frac{5 x}{3} + 7 = \frac{17}{6} + \frac{- 5 x}{2}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{5 x}{3} + 7 = \frac{17}{6} - \frac{5 x}{2}$

Step 3

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

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Step 3.1

Add $\frac{5 x}{2}$ to both sides of the equation.

$- \frac{5 x}{3} + 7 + \frac{5 x}{2} = \frac{17}{6}$

Step 3.2

To write $- \frac{5 x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5 x}{3} \cdot \frac{2}{2} + \frac{5 x}{2} + 7 = \frac{17}{6}$

Step 3.3

To write $\frac{5 x}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{5 x}{3} \cdot \frac{2}{2} + \frac{5 x}{2} \cdot \frac{3}{3} + 7 = \frac{17}{6}$

Step 3.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{5 x}{3}$ by $\frac{2}{2}$ .

$- \frac{5 x \cdot 2}{3 \cdot 2} + \frac{5 x}{2} \cdot \frac{3}{3} + 7 = \frac{17}{6}$

Step 3.4.2

Multiply $3$ by $2$ .

$- \frac{5 x \cdot 2}{6} + \frac{5 x}{2} \cdot \frac{3}{3} + 7 = \frac{17}{6}$

Step 3.4.3

Multiply $\frac{5 x}{2}$ by $\frac{3}{3}$ .

$- \frac{5 x \cdot 2}{6} + \frac{5 x \cdot 3}{2 \cdot 3} + 7 = \frac{17}{6}$

Step 3.4.4

Multiply $2$ by $3$ .

$- \frac{5 x \cdot 2}{6} + \frac{5 x \cdot 3}{6} + 7 = \frac{17}{6}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 5 x \cdot 2 + 5 x \cdot 3}{6} + 7 = \frac{17}{6}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Factor $5 x$ out of $- 5 x \cdot 2 + 5 x \cdot 3$ .

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Step 3.6.1.1

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

$\frac{5 x (- 1 \cdot 2) + 5 x \cdot 3}{6} + 7 = \frac{17}{6}$

Step 3.6.1.2

Factor $5 x$ out of $5 x \cdot 3$ .

$\frac{5 x (- 1 \cdot 2) + 5 x (3)}{6} + 7 = \frac{17}{6}$

Step 3.6.1.3

Factor $5 x$ out of $5 x (- 1 \cdot 2) + 5 x (3)$ .

$\frac{5 x (- 1 \cdot 2 + 3)}{6} + 7 = \frac{17}{6}$

Step 3.6.2

Multiply $- 1$ by $2$ .

$\frac{5 x (- 2 + 3)}{6} + 7 = \frac{17}{6}$

Step 3.6.3

Add $- 2$ and $3$ .

$\frac{5 x \cdot 1}{6} + 7 = \frac{17}{6}$

Step 3.6.4

Multiply $5$ by $1$ .

$\frac{5 x}{6} + 7 = \frac{17}{6}$

Step 4

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

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Step 4.1

Subtract $7$ from both sides of the equation.

$\frac{5 x}{6} = \frac{17}{6} - 7$

Step 4.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 x}{6} = \frac{17}{6} - 7 \cdot \frac{6}{6}$

Step 4.3

Combine $- 7$ and $\frac{6}{6}$ .

$\frac{5 x}{6} = \frac{17}{6} + \frac{- 7 \cdot 6}{6}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{5 x}{6} = \frac{17 - 7 \cdot 6}{6}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 7$ by $6$ .

$\frac{5 x}{6} = \frac{17 - 42}{6}$

Step 4.5.2

Subtract $42$ from $17$ .

$\frac{5 x}{6} = \frac{- 25}{6}$

Step 4.6

Move the negative in front of the fraction.

$\frac{5 x}{6} = - \frac{25}{6}$

Step 5

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

$5 x = - 25$

Step 6

Divide each term in $5 x = - 25$ by $5$ and simplify.

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Step 6.1

Divide each term in $5 x = - 25$ by $5$ .

$\frac{5 x}{5} = \frac{- 25}{5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 25}{5}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 25}{5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 25$ by $5$ .

$x = - 5$