Algebra Examples

$\frac{5}{6} (x + 9) + \frac{3}{4} (x + 1) - \frac{7}{9} = 8$

Step 1

Simplify $\frac{5}{6} \cdot (x + 9) + \frac{3}{4} \cdot (x + 1) - \frac{7}{9}$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$\frac{5}{6} x + \frac{5}{6} \cdot 9 + \frac{3}{4} \cdot (x + 1) - \frac{7}{9} = 8$

Step 1.1.2

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

$\frac{5 x}{6} + \frac{5}{6} \cdot 9 + \frac{3}{4} \cdot (x + 1) - \frac{7}{9} = 8$

Step 1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.1.3.1

Factor $3$ out of $6$ .

$\frac{5 x}{6} + \frac{5}{3 (2)} \cdot 9 + \frac{3}{4} \cdot (x + 1) - \frac{7}{9} = 8$

Step 1.1.3.2

Factor $3$ out of $9$ .

$\frac{5 x}{6} + \frac{5}{3 \cdot 2} \cdot (3 \cdot 3) + \frac{3}{4} \cdot (x + 1) - \frac{7}{9} = 8$

Step 1.1.3.3

Cancel the common factor.

$\frac{5 x}{6} + \frac{5}{3 \cdot 2} \cdot (3 \cdot 3) + \frac{3}{4} \cdot (x + 1) - \frac{7}{9} = 8$

Step 1.1.3.4

Rewrite the expression.

$\frac{5 x}{6} + \frac{5}{2} \cdot 3 + \frac{3}{4} \cdot (x + 1) - \frac{7}{9} = 8$

Step 1.1.4

Combine $\frac{5}{2}$ and $3$ .

$\frac{5 x}{6} + \frac{5 \cdot 3}{2} + \frac{3}{4} \cdot (x + 1) - \frac{7}{9} = 8$

Step 1.1.5

Multiply $5$ by $3$ .

$\frac{5 x}{6} + \frac{15}{2} + \frac{3}{4} \cdot (x + 1) - \frac{7}{9} = 8$

Step 1.1.6

Apply the distributive property.

$\frac{5 x}{6} + \frac{15}{2} + \frac{3}{4} x + \frac{3}{4} \cdot 1 - \frac{7}{9} = 8$

Step 1.1.7

Combine $\frac{3}{4}$ and $x$ .

$\frac{5 x}{6} + \frac{15}{2} + \frac{3 x}{4} + \frac{3}{4} \cdot 1 - \frac{7}{9} = 8$

Step 1.1.8

Multiply $\frac{3}{4}$ by $1$ .

$\frac{5 x}{6} + \frac{15}{2} + \frac{3 x}{4} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.2

To write $\frac{5 x}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{6} \cdot \frac{2}{2} + \frac{3 x}{4} + \frac{15}{2} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.3

To write $\frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 x}{6} \cdot \frac{2}{2} + \frac{3 x}{4} \cdot \frac{3}{3} + \frac{15}{2} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.4.1

Multiply $\frac{5 x}{6}$ by $\frac{2}{2}$ .

$\frac{5 x \cdot 2}{6 \cdot 2} + \frac{3 x}{4} \cdot \frac{3}{3} + \frac{15}{2} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.4.2

Multiply $6$ by $2$ .

$\frac{5 x \cdot 2}{12} + \frac{3 x}{4} \cdot \frac{3}{3} + \frac{15}{2} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.4.3

Multiply $\frac{3 x}{4}$ by $\frac{3}{3}$ .

$\frac{5 x \cdot 2}{12} + \frac{3 x \cdot 3}{4 \cdot 3} + \frac{15}{2} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.4.4

Multiply $4$ by $3$ .

$\frac{5 x \cdot 2}{12} + \frac{3 x \cdot 3}{12} + \frac{15}{2} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.5

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 + 3 x \cdot 3}{12} + \frac{15}{2} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.6

Find the common denominator.

Tap for more steps...

Step 1.6.1

Multiply $\frac{5 x \cdot 2 + 3 x \cdot 3}{12}$ by $\frac{3}{3}$ .

$\frac{5 x \cdot 2 + 3 x \cdot 3}{12} \cdot \frac{3}{3} + \frac{15}{2} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.6.2

Multiply $\frac{5 x \cdot 2 + 3 x \cdot 3}{12}$ by $\frac{3}{3}$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{12 \cdot 3} + \frac{15}{2} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.6.3

Multiply $\frac{15}{2}$ by $\frac{18}{18}$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{12 \cdot 3} + \frac{15}{2} \cdot \frac{18}{18} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.6.4

Multiply $\frac{15}{2}$ by $\frac{18}{18}$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{12 \cdot 3} + \frac{15 \cdot 18}{2 \cdot 18} + \frac{3}{4} - \frac{7}{9} = 8$

Step 1.6.5

Multiply $\frac{3}{4}$ by $\frac{9}{9}$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{12 \cdot 3} + \frac{15 \cdot 18}{2 \cdot 18} + \frac{3}{4} \cdot \frac{9}{9} - \frac{7}{9} = 8$

Step 1.6.6

Multiply $\frac{3}{4}$ by $\frac{9}{9}$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{12 \cdot 3} + \frac{15 \cdot 18}{2 \cdot 18} + \frac{3 \cdot 9}{4 \cdot 9} - \frac{7}{9} = 8$

Step 1.6.7

Multiply $\frac{7}{9}$ by $\frac{4}{4}$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{12 \cdot 3} + \frac{15 \cdot 18}{2 \cdot 18} + \frac{3 \cdot 9}{4 \cdot 9} - (\frac{7}{9} \cdot \frac{4}{4}) = 8$

Step 1.6.8

Multiply $\frac{7}{9}$ by $\frac{4}{4}$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{12 \cdot 3} + \frac{15 \cdot 18}{2 \cdot 18} + \frac{3 \cdot 9}{4 \cdot 9} - \frac{7 \cdot 4}{9 \cdot 4} = 8$

Step 1.6.9

Reorder the factors of $12 \cdot 3$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{3 \cdot 12} + \frac{15 \cdot 18}{2 \cdot 18} + \frac{3 \cdot 9}{4 \cdot 9} - \frac{7 \cdot 4}{9 \cdot 4} = 8$

Step 1.6.10

Multiply $3$ by $12$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{36} + \frac{15 \cdot 18}{2 \cdot 18} + \frac{3 \cdot 9}{4 \cdot 9} - \frac{7 \cdot 4}{9 \cdot 4} = 8$

Step 1.6.11

Multiply $2$ by $18$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{36} + \frac{15 \cdot 18}{36} + \frac{3 \cdot 9}{4 \cdot 9} - \frac{7 \cdot 4}{9 \cdot 4} = 8$

Step 1.6.12

Multiply $4$ by $9$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{36} + \frac{15 \cdot 18}{36} + \frac{3 \cdot 9}{36} - \frac{7 \cdot 4}{9 \cdot 4} = 8$

Step 1.6.13

Reorder the factors of $9 \cdot 4$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{36} + \frac{15 \cdot 18}{36} + \frac{3 \cdot 9}{36} - \frac{7 \cdot 4}{4 \cdot 9} = 8$

Step 1.6.14

Multiply $4$ by $9$ .

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3}{36} + \frac{15 \cdot 18}{36} + \frac{3 \cdot 9}{36} - \frac{7 \cdot 4}{36} = 8$

Step 1.7

Combine the numerators over the common denominator.

$\frac{(5 x \cdot 2 + 3 x \cdot 3) \cdot 3 + 15 \cdot 18 + 3 \cdot 9 - 7 \cdot 4}{36} = 8$

Step 1.8

Simplify each term.

Tap for more steps...

Step 1.8.1

Simplify each term.

Tap for more steps...

Step 1.8.1.1

Multiply $2$ by $5$ .

$\frac{(10 x + 3 x \cdot 3) \cdot 3 + 15 \cdot 18 + 3 \cdot 9 - 7 \cdot 4}{36} = 8$

Step 1.8.1.2

Multiply $3$ by $3$ .

$\frac{(10 x + 9 x) \cdot 3 + 15 \cdot 18 + 3 \cdot 9 - 7 \cdot 4}{36} = 8$

Step 1.8.2

Add $10 x$ and $9 x$ .

$\frac{19 x \cdot 3 + 15 \cdot 18 + 3 \cdot 9 - 7 \cdot 4}{36} = 8$

Step 1.8.3

Multiply $3$ by $19$ .

$\frac{57 x + 15 \cdot 18 + 3 \cdot 9 - 7 \cdot 4}{36} = 8$

Step 1.8.4

Multiply $15$ by $18$ .

$\frac{57 x + 270 + 3 \cdot 9 - 7 \cdot 4}{36} = 8$

Step 1.8.5

Multiply $3$ by $9$ .

$\frac{57 x + 270 + 27 - 7 \cdot 4}{36} = 8$

Step 1.8.6

Multiply $- 7$ by $4$ .

$\frac{57 x + 270 + 27 - 28}{36} = 8$

Step 1.9

Simplify by adding and subtracting.

Tap for more steps...

Step 1.9.1

Add $270$ and $27$ .

$\frac{57 x + 297 - 28}{36} = 8$

Step 1.9.2

Subtract $28$ from $297$ .

$\frac{57 x + 269}{36} = 8$

Step 2

Multiply both sides by $36$ .

$\frac{57 x + 269}{36} \cdot 36 = 8 \cdot 36$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $36$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$\frac{57 x + 269}{36} \cdot 36 = 8 \cdot 36$

Step 3.1.1.2

Rewrite the expression.

$57 x + 269 = 8 \cdot 36$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $8$ by $36$ .

$57 x + 269 = 288$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Subtract $269$ from both sides of the equation.

$57 x = 288 - 269$

Step 4.1.2

Subtract $269$ from $288$ .

$57 x = 19$

Step 4.2

Divide each term in $57 x = 19$ by $57$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $57 x = 19$ by $57$ .

$\frac{57 x}{57} = \frac{19}{57}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $57$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{57 x}{57} = \frac{19}{57}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{19}{57}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Cancel the common factor of $19$ and $57$ .

Tap for more steps...

Step 4.2.3.1.1

Factor $19$ out of $19$ .

$x = \frac{19 (1)}{57}$

Step 4.2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 4.2.3.1.2.1

Factor $19$ out of $57$ .

$x = \frac{19 \cdot 1}{19 \cdot 3}$

Step 4.2.3.1.2.2

Cancel the common factor.

$x = \frac{19 \cdot 1}{19 \cdot 3}$

Step 4.2.3.1.2.3

Rewrite the expression.

$x = \frac{1}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}$

Decimal Form:

$x = 0.\overline{3}$