Pre-Algebra Examples

$\frac{5}{6} \cdot (6 x + 12) + 1 = \frac{2}{3} \cdot (9 x - 3) + 5$

Step 1

Simplify $\frac{5}{6} \cdot (6 x + 12) + 1$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$\frac{5}{6} (6 x) + \frac{5}{6} \cdot 12 + 1 = \frac{2}{3} \cdot (9 x - 3) + 5$

Step 1.1.2

Cancel the common factor of $6$ .

Tap for more steps...

Step 1.1.2.1

Factor $6$ out of $6 x$ .

$\frac{5}{6} (6 (x)) + \frac{5}{6} \cdot 12 + 1 = \frac{2}{3} \cdot (9 x - 3) + 5$

Step 1.1.2.2

Cancel the common factor.

$\frac{5}{6} (6 x) + \frac{5}{6} \cdot 12 + 1 = \frac{2}{3} \cdot (9 x - 3) + 5$

Step 1.1.2.3

Rewrite the expression.

$5 x + \frac{5}{6} \cdot 12 + 1 = \frac{2}{3} \cdot (9 x - 3) + 5$

Step 1.1.3

Cancel the common factor of $6$ .

Tap for more steps...

Step 1.1.3.1

Factor $6$ out of $12$ .

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

Step 1.1.3.2

Cancel the common factor.

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

Step 1.1.3.3

Rewrite the expression.

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

Step 1.1.4

Multiply $5$ by $2$ .

$5 x + 10 + 1 = \frac{2}{3} \cdot (9 x - 3) + 5$

Step 1.2

Add $10$ and $1$ .

$5 x + 11 = \frac{2}{3} \cdot (9 x - 3) + 5$

Step 2

Simplify $\frac{2}{3} \cdot (9 x - 3) + 5$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$5 x + 11 = \frac{2}{3} (9 x) + \frac{2}{3} \cdot - 3 + 5$

Step 2.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.2.1

Factor $3$ out of $9 x$ .

$5 x + 11 = \frac{2}{3} (3 (3 x)) + \frac{2}{3} \cdot - 3 + 5$

Step 2.1.2.2

Cancel the common factor.

$5 x + 11 = \frac{2}{3} (3 (3 x)) + \frac{2}{3} \cdot - 3 + 5$

Step 2.1.2.3

Rewrite the expression.

$5 x + 11 = 2 (3 x) + \frac{2}{3} \cdot - 3 + 5$

Step 2.1.3

Multiply $3$ by $2$ .

$5 x + 11 = 6 x + \frac{2}{3} \cdot - 3 + 5$

Step 2.1.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.4.1

Factor $3$ out of $- 3$ .

$5 x + 11 = 6 x + \frac{2}{3} \cdot (3 (- 1)) + 5$

Step 2.1.4.2

Cancel the common factor.

$5 x + 11 = 6 x + \frac{2}{3} \cdot (3 \cdot - 1) + 5$

Step 2.1.4.3

Rewrite the expression.

$5 x + 11 = 6 x + 2 \cdot - 1 + 5$

Step 2.1.5

Multiply $2$ by $- 1$ .

$5 x + 11 = 6 x - 2 + 5$

Step 2.2

Add $- 2$ and $5$ .

$5 x + 11 = 6 x + 3$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 8$

Step 4