Pre-Algebra Examples

$\frac{5}{6} x - 2 + \frac{1}{3} x = \frac{7}{24} x + \frac{1}{8}$

Step 1

Simplify $\frac{5}{6} x - 2 + \frac{1}{3} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{5}{6}$ and $x$ .

$\frac{5 x}{6} - 2 + \frac{1}{3} x = \frac{7}{24} x + \frac{1}{8}$

Step 1.1.2

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

$\frac{5 x}{6} - 2 + \frac{x}{3} = \frac{7}{24} x + \frac{1}{8}$

Step 1.2

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

$\frac{5 x}{6} + \frac{x}{3} \cdot \frac{2}{2} - 2 = \frac{7}{24} x + \frac{1}{8}$

Step 1.3

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

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Step 1.3.1

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

$\frac{5 x}{6} + \frac{x \cdot 2}{3 \cdot 2} - 2 = \frac{7}{24} x + \frac{1}{8}$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{5 x}{6} + \frac{x \cdot 2}{6} - 2 = \frac{7}{24} x + \frac{1}{8}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{5 x + x \cdot 2}{6} - 2 = \frac{7}{24} x + \frac{1}{8}$

Step 1.5

Add $5 x$ and $x \cdot 2$ .

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Step 1.5.1

Reorder $x$ and $2$ .

$\frac{5 x + 2 \cdot x}{6} - 2 = \frac{7}{24} x + \frac{1}{8}$

Step 1.5.2

Add $5 x$ and $2 \cdot x$ .

$\frac{7 x}{6} - 2 = \frac{7}{24} x + \frac{1}{8}$

Step 2

Combine $\frac{7}{24}$ and $x$ .

$\frac{7 x}{6} - 2 = \frac{7 x}{24} + \frac{1}{8}$

Step 3

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

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Step 3.1

Subtract $\frac{7 x}{24}$ from both sides of the equation.

$\frac{7 x}{6} - 2 - \frac{7 x}{24} = \frac{1}{8}$

Step 3.2

To write $\frac{7 x}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7 x}{6} \cdot \frac{4}{4} - \frac{7 x}{24} - 2 = \frac{1}{8}$

Step 3.3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{7 x}{6}$ by $\frac{4}{4}$ .

$\frac{7 x \cdot 4}{6 \cdot 4} - \frac{7 x}{24} - 2 = \frac{1}{8}$

Step 3.3.2

Multiply $6$ by $4$ .

$\frac{7 x \cdot 4}{24} - \frac{7 x}{24} - 2 = \frac{1}{8}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{7 x \cdot 4 - 7 x}{24} - 2 = \frac{1}{8}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $7 x$ out of $7 x \cdot 4 - 7 x$ .

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Step 3.5.1.1.1

Factor $7 x$ out of $7 x \cdot 4$ .

$\frac{7 x (4) - 7 x}{24} - 2 = \frac{1}{8}$

Step 3.5.1.1.2

Factor $7 x$ out of $- 7 x$ .

$\frac{7 x (4) + 7 x (- 1)}{24} - 2 = \frac{1}{8}$

Step 3.5.1.1.3

Factor $7 x$ out of $7 x (4) + 7 x (- 1)$ .

$\frac{7 x (4 - 1)}{24} - 2 = \frac{1}{8}$

Step 3.5.1.2

Subtract $1$ from $4$ .

$\frac{7 x \cdot 3}{24} - 2 = \frac{1}{8}$

Step 3.5.1.3

Multiply $3$ by $7$ .

$\frac{21 x}{24} - 2 = \frac{1}{8}$

Step 3.5.2

Cancel the common factor of $21$ and $24$ .

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Step 3.5.2.1

Factor $3$ out of $21 x$ .

$\frac{3 (7 x)}{24} - 2 = \frac{1}{8}$

Step 3.5.2.2

Cancel the common factors.

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Step 3.5.2.2.1

Factor $3$ out of $24$ .

$\frac{3 (7 x)}{3 (8)} - 2 = \frac{1}{8}$

Step 3.5.2.2.2

Cancel the common factor.

$\frac{3 (7 x)}{3 \cdot 8} - 2 = \frac{1}{8}$

Step 3.5.2.2.3

Rewrite the expression.

$\frac{7 x}{8} - 2 = \frac{1}{8}$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$\frac{7 x}{8} = \frac{1}{8} + 2$

Step 4.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{7 x}{8} = \frac{1}{8} + 2 \cdot \frac{8}{8}$

Step 4.3

Combine $2$ and $\frac{8}{8}$ .

$\frac{7 x}{8} = \frac{1}{8} + \frac{2 \cdot 8}{8}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{7 x}{8} = \frac{1 + 2 \cdot 8}{8}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $2$ by $8$ .

$\frac{7 x}{8} = \frac{1 + 16}{8}$

Step 4.5.2

Add $1$ and $16$ .

$\frac{7 x}{8} = \frac{17}{8}$

Step 5

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

$7 x = 17$

Step 6

Divide each term in $7 x = 17$ by $7$ and simplify.

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Step 6.1

Divide each term in $7 x = 17$ by $7$ .

$\frac{7 x}{7} = \frac{17}{7}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $7$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{17}{7}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{17}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{17}{7}$

Decimal Form:

$x = 2.\overline{428571}$

Mixed Number Form:

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