Algebra Examples

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

Step 1

Simplify $\frac{1}{2} x + \frac{1}{3} x - 7$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{2}$ and $x$ .

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

Step 1.1.2

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

Multiply $2$ by $3$ .

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

Step 1.4.3

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

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

Step 1.4.4

Multiply $3$ by $2$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Reorder $x$ and $2$ .

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

Step 1.7

Add $3 \cdot x$ and $2 \cdot x$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

Subtract $\frac{5 x}{6}$ from both sides of the equation.

$\frac{5 x}{6} - 7 - \frac{5 x}{6} = 0$

Step 3.2

Combine the opposite terms in $\frac{5 x}{6} - 7 - \frac{5 x}{6}$ .

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Step 3.2.1

Subtract $\frac{5 x}{6}$ from $\frac{5 x}{6}$ .

$0 - 7 = 0$

Step 3.2.2

Subtract $7$ from $0$ .

$- 7 = 0$

Step 4

Since $- 7 \neq 0$ , there are no solutions.

No solution