Algebra Examples

$\frac{3}{8} x - \frac{1}{3} x + 6 = \frac{1}{6} x$

Step 1

Simplify $\frac{3}{8} x - \frac{1}{3} x + 6$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{3 x}{8} - \frac{1}{3} x + 6 = \frac{1}{6} x$

Step 1.1.2

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

$\frac{3 x}{8} - \frac{x}{3} + 6 = \frac{1}{6} x$

Step 1.2

To write $\frac{3 x}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x}{8} \cdot \frac{3}{3} - \frac{x}{3} + 6 = \frac{1}{6} x$

Step 1.3

To write $- \frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{3 x}{8} \cdot \frac{3}{3} - \frac{x}{3} \cdot \frac{8}{8} + 6 = \frac{1}{6} x$

Step 1.4

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

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Step 1.4.1

Multiply $\frac{3 x}{8}$ by $\frac{3}{3}$ .

$\frac{3 x \cdot 3}{8 \cdot 3} - \frac{x}{3} \cdot \frac{8}{8} + 6 = \frac{1}{6} x$

Step 1.4.2

Multiply $8$ by $3$ .

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

Step 1.4.3

Multiply $\frac{x}{3}$ by $\frac{8}{8}$ .

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

Step 1.4.4

Multiply $3$ by $8$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $x$ out of $3 x \cdot 3 - x \cdot 8$ .

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Step 1.6.1.1.1

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

$\frac{x (3 \cdot 3) - x \cdot 8}{24} + 6 = \frac{1}{6} x$

Step 1.6.1.1.2

Factor $x$ out of $- x \cdot 8$ .

$\frac{x (3 \cdot 3) + x (- 1 \cdot 8)}{24} + 6 = \frac{1}{6} x$

Step 1.6.1.1.3

Factor $x$ out of $x (3 \cdot 3) + x (- 1 \cdot 8)$ .

$\frac{x (3 \cdot 3 - 1 \cdot 8)}{24} + 6 = \frac{1}{6} x$

Step 1.6.1.2

Multiply $3$ by $3$ .

$\frac{x (9 - 1 \cdot 8)}{24} + 6 = \frac{1}{6} x$

Step 1.6.1.3

Multiply $- 1$ by $8$ .

$\frac{x (9 - 8)}{24} + 6 = \frac{1}{6} x$

Step 1.6.1.4

Subtract $8$ from $9$ .

$\frac{x \cdot 1}{24} + 6 = \frac{1}{6} x$

Step 1.6.2

Multiply $x$ by $1$ .

$\frac{x}{24} + 6 = \frac{1}{6} x$

Step 2

Combine $\frac{1}{6}$ and $x$ .

$\frac{x}{24} + 6 = \frac{x}{6}$

Step 3

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

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Step 3.1

Subtract $\frac{x}{6}$ from both sides of the equation.

$\frac{x}{24} + 6 - \frac{x}{6} = 0$

Step 3.2

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

$\frac{x}{24} - \frac{x}{6} \cdot \frac{4}{4} + 6 = 0$

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

$\frac{x}{24} - \frac{x \cdot 4}{6 \cdot 4} + 6 = 0$

Step 3.3.2

Multiply $6$ by $4$ .

$\frac{x}{24} - \frac{x \cdot 4}{24} + 6 = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{x - x \cdot 4}{24} + 6 = 0$

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

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Step 3.5.1.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 4}{24} + 6 = 0$

Step 3.5.1.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 4}{24} + 6 = 0$

Step 3.5.1.1.3

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

$\frac{x \cdot 1 + x (- 1 \cdot 4)}{24} + 6 = 0$

Step 3.5.1.1.4

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

$\frac{x (1 - 1 \cdot 4)}{24} + 6 = 0$

Step 3.5.1.2

Multiply $- 1$ by $4$ .

$\frac{x (1 - 4)}{24} + 6 = 0$

Step 3.5.1.3

Subtract $4$ from $1$ .

$\frac{x \cdot - 3}{24} + 6 = 0$

Step 3.5.2

Cancel the common factor of $- 3$ and $24$ .

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Step 3.5.2.1

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

$\frac{3 (x \cdot - 1)}{24} + 6 = 0$

Step 3.5.2.2

Cancel the common factors.

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Step 3.5.2.2.1

Factor $3$ out of $24$ .

$\frac{3 (x \cdot - 1)}{3 (8)} + 6 = 0$

Step 3.5.2.2.2

Cancel the common factor.

$\frac{3 (x \cdot - 1)}{3 \cdot 8} + 6 = 0$

Step 3.5.2.2.3

Rewrite the expression.

$\frac{x \cdot - 1}{8} + 6 = 0$

Step 3.5.3

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{8} + 6 = 0$

Step 3.5.4

Move the negative in front of the fraction.

$- \frac{x}{8} + 6 = 0$

Step 4

Subtract $6$ from both sides of the equation.

$- \frac{x}{8} = - 6$

Step 5

Multiply both sides of the equation by $- 8$ .

$- 8 (- \frac{x}{8}) = - 8 \cdot - 6$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- 8 (- \frac{x}{8})$ .

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Step 6.1.1.1

Cancel the common factor of $8$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{x}{8}$ into the numerator.

$- 8 \frac{- x}{8} = - 8 \cdot - 6$

Step 6.1.1.1.2

Factor $8$ out of $- 8$ .

$8 (- 1) \frac{- x}{8} = - 8 \cdot - 6$

Step 6.1.1.1.3

Cancel the common factor.

$8 \cdot - 1 \frac{- x}{8} = - 8 \cdot - 6$

Step 6.1.1.1.4

Rewrite the expression.

$- - x = - 8 \cdot - 6$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 8 \cdot - 6$

Step 6.1.1.2.2

Multiply $x$ by $1$ .

$x = - 8 \cdot - 6$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 8$ by $- 6$ .

$x = 48$