Algebra Examples

$\frac{5}{6} x - \frac{1}{5} x + 4 = \frac{7}{10} x$

Step 1

Simplify $\frac{5}{6} x - \frac{1}{5} x + 4$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{5 x}{6} - \frac{1}{5} x + 4 = \frac{7}{10} x$

Step 1.1.2

Combine $x$ and $\frac{1}{5}$ .

$\frac{5 x}{6} - \frac{x}{5} + 4 = \frac{7}{10} x$

Step 1.2

To write $\frac{5 x}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 x}{6} \cdot \frac{5}{5} - \frac{x}{5} + 4 = \frac{7}{10} x$

Step 1.3

To write $- \frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 x}{6} \cdot \frac{5}{5} - \frac{x}{5} \cdot \frac{6}{6} + 4 = \frac{7}{10} x$

Step 1.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{5 x}{6}$ by $\frac{5}{5}$ .

$\frac{5 x \cdot 5}{6 \cdot 5} - \frac{x}{5} \cdot \frac{6}{6} + 4 = \frac{7}{10} x$

Step 1.4.2

Multiply $6$ by $5$ .

$\frac{5 x \cdot 5}{30} - \frac{x}{5} \cdot \frac{6}{6} + 4 = \frac{7}{10} x$

Step 1.4.3

Multiply $\frac{x}{5}$ by $\frac{6}{6}$ .

$\frac{5 x \cdot 5}{30} - \frac{x \cdot 6}{5 \cdot 6} + 4 = \frac{7}{10} x$

Step 1.4.4

Multiply $5$ by $6$ .

$\frac{5 x \cdot 5}{30} - \frac{x \cdot 6}{30} + 4 = \frac{7}{10} x$

Step 1.5

Combine the numerators over the common denominator.

$\frac{5 x \cdot 5 - x \cdot 6}{30} + 4 = \frac{7}{10} x$

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 $5 x \cdot 5 - x \cdot 6$ .

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Step 1.6.1.1.1

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

$\frac{x (5 \cdot 5) - x \cdot 6}{30} + 4 = \frac{7}{10} x$

Step 1.6.1.1.2

Factor $x$ out of $- x \cdot 6$ .

$\frac{x (5 \cdot 5) + x (- 1 \cdot 6)}{30} + 4 = \frac{7}{10} x$

Step 1.6.1.1.3

Factor $x$ out of $x (5 \cdot 5) + x (- 1 \cdot 6)$ .

$\frac{x (5 \cdot 5 - 1 \cdot 6)}{30} + 4 = \frac{7}{10} x$

Step 1.6.1.2

Multiply $5$ by $5$ .

$\frac{x (25 - 1 \cdot 6)}{30} + 4 = \frac{7}{10} x$

Step 1.6.1.3

Multiply $- 1$ by $6$ .

$\frac{x (25 - 6)}{30} + 4 = \frac{7}{10} x$

Step 1.6.1.4

Subtract $6$ from $25$ .

$\frac{x \cdot 19}{30} + 4 = \frac{7}{10} x$

Step 1.6.2

Move $19$ to the left of $x$ .

$\frac{19 x}{30} + 4 = \frac{7}{10} x$

Step 2

Combine $\frac{7}{10}$ and $x$ .

$\frac{19 x}{30} + 4 = \frac{7 x}{10}$

Step 3

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

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Step 3.1

Subtract $\frac{7 x}{10}$ from both sides of the equation.

$\frac{19 x}{30} + 4 - \frac{7 x}{10} = 0$

Step 3.2

To write $- \frac{7 x}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{19 x}{30} - \frac{7 x}{10} \cdot \frac{3}{3} + 4 = 0$

Step 3.3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{7 x}{10}$ by $\frac{3}{3}$ .

$\frac{19 x}{30} - \frac{7 x \cdot 3}{10 \cdot 3} + 4 = 0$

Step 3.3.2

Multiply $10$ by $3$ .

$\frac{19 x}{30} - \frac{7 x \cdot 3}{30} + 4 = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{19 x - 7 x \cdot 3}{30} + 4 = 0$

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 $19 x - 7 x \cdot 3$ .

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Step 3.5.1.1.1

Factor $x$ out of $19 x$ .

$\frac{x \cdot 19 - 7 x \cdot 3}{30} + 4 = 0$

Step 3.5.1.1.2

Factor $x$ out of $- 7 x \cdot 3$ .

$\frac{x \cdot 19 + x (- 7 \cdot 3)}{30} + 4 = 0$

Step 3.5.1.1.3

Factor $x$ out of $x \cdot 19 + x (- 7 \cdot 3)$ .

$\frac{x (19 - 7 \cdot 3)}{30} + 4 = 0$

Step 3.5.1.2

Multiply $- 7$ by $3$ .

$\frac{x (19 - 21)}{30} + 4 = 0$

Step 3.5.1.3

Subtract $21$ from $19$ .

$\frac{x \cdot - 2}{30} + 4 = 0$

Step 3.5.2

Cancel the common factor of $- 2$ and $30$ .

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Step 3.5.2.1

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

$\frac{2 (x \cdot - 1)}{30} + 4 = 0$

Step 3.5.2.2

Cancel the common factors.

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Step 3.5.2.2.1

Factor $2$ out of $30$ .

$\frac{2 (x \cdot - 1)}{2 (15)} + 4 = 0$

Step 3.5.2.2.2

Cancel the common factor.

$\frac{2 (x \cdot - 1)}{2 \cdot 15} + 4 = 0$

Step 3.5.2.2.3

Rewrite the expression.

$\frac{x \cdot - 1}{15} + 4 = 0$

Step 3.5.3

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

$\frac{- 1 \cdot x}{15} + 4 = 0$

Step 3.5.4

Move the negative in front of the fraction.

$- \frac{x}{15} + 4 = 0$

Step 4

Subtract $4$ from both sides of the equation.

$- \frac{x}{15} = - 4$

Step 5

Multiply both sides of the equation by $- 15$ .

$- 15 (- \frac{x}{15}) = - 15 \cdot - 4$

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 $- 15 (- \frac{x}{15})$ .

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Step 6.1.1.1

Cancel the common factor of $15$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{x}{15}$ into the numerator.

$- 15 \frac{- x}{15} = - 15 \cdot - 4$

Step 6.1.1.1.2

Factor $15$ out of $- 15$ .

$15 (- 1) \frac{- x}{15} = - 15 \cdot - 4$

Step 6.1.1.1.3

Cancel the common factor.

$15 \cdot - 1 \frac{- x}{15} = - 15 \cdot - 4$

Step 6.1.1.1.4

Rewrite the expression.

$- - x = - 15 \cdot - 4$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 15 \cdot - 4$

Step 6.1.1.2.2

Multiply $x$ by $1$ .

$x = - 15 \cdot - 4$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 15$ by $- 4$ .

$x = 60$