Algebra Examples

$\frac{10}{15} = \frac{6 x + 2}{4 x + 7}$

Step 1

Rewrite the equation as $\frac{6 x + 2}{4 x + 7} = \frac{10}{15}$ .

$\frac{6 x + 2}{4 x + 7} = \frac{10}{15}$

Step 2

Simplify both sides.

Tap for more steps...

Step 2.1

Factor $2$ out of $6 x + 2$ .

Tap for more steps...

Step 2.1.1

Factor $2$ out of $6 x$ .

$\frac{2 (3 x) + 2}{4 x + 7} = \frac{10}{15}$

Step 2.1.2

Factor $2$ out of $2$ .

$\frac{2 (3 x) + 2 (1)}{4 x + 7} = \frac{10}{15}$

Step 2.1.3

Factor $2$ out of $2 (3 x) + 2 (1)$ .

$\frac{2 (3 x + 1)}{4 x + 7} = \frac{10}{15}$

Step 2.2

Cancel the common factor of $10$ and $15$ .

Tap for more steps...

Step 2.2.1

Factor $5$ out of $10$ .

$\frac{2 (3 x + 1)}{4 x + 7} = \frac{5 (2)}{15}$

Step 2.2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.2.1

Factor $5$ out of $15$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

$\frac{2 (3 x + 1)}{4 x + 7} = \frac{2}{3}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$2 (3 x + 1) \cdot 3 = (4 x + 7) \cdot 2$

Step 4

Solve the equation for $x$ .

Tap for more steps...

Step 4.1

Simplify $2 (3 x + 1) \cdot 3$ .

Tap for more steps...

Step 4.1.1

Rewrite.

$0 + 0 + 2 (3 x + 1) \cdot 3 = (4 x + 7) \cdot 2$

Step 4.1.2

Simplify by adding zeros.

$2 (3 x + 1) \cdot 3 = (4 x + 7) \cdot 2$

Step 4.1.3

Apply the distributive property.

$(2 (3 x) + 2 \cdot 1) \cdot 3 = (4 x + 7) \cdot 2$

Step 4.1.4

Multiply.

Tap for more steps...

Step 4.1.4.1

Multiply $3$ by $2$ .

$(6 x + 2 \cdot 1) \cdot 3 = (4 x + 7) \cdot 2$

Step 4.1.4.2

Multiply $2$ by $1$ .

$(6 x + 2) \cdot 3 = (4 x + 7) \cdot 2$

Step 4.1.5

Apply the distributive property.

$6 x \cdot 3 + 2 \cdot 3 = (4 x + 7) \cdot 2$

Step 4.1.6

Multiply.

Tap for more steps...

Step 4.1.6.1

Multiply $3$ by $6$ .

$18 x + 2 \cdot 3 = (4 x + 7) \cdot 2$

Step 4.1.6.2

Multiply $2$ by $3$ .

$18 x + 6 = (4 x + 7) \cdot 2$

Step 4.2

Simplify $(4 x + 7) \cdot 2$ .

Tap for more steps...

Step 4.2.1

Apply the distributive property.

$18 x + 6 = 4 x \cdot 2 + 7 \cdot 2$

Step 4.2.2

Multiply.

Tap for more steps...

Step 4.2.2.1

Multiply $2$ by $4$ .

$18 x + 6 = 8 x + 7 \cdot 2$

Step 4.2.2.2

Multiply $7$ by $2$ .

$18 x + 6 = 8 x + 14$

Step 4.3

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

Tap for more steps...

Step 4.3.1

Subtract $8 x$ from both sides of the equation.

$18 x + 6 - 8 x = 14$

Step 4.3.2

Subtract $8 x$ from $18 x$ .

$10 x + 6 = 14$

Step 4.4

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

Tap for more steps...

Step 4.4.1

Subtract $6$ from both sides of the equation.

$10 x = 14 - 6$

Step 4.4.2

Subtract $6$ from $14$ .

$10 x = 8$

Step 4.5

Divide each term in $10 x = 8$ by $10$ and simplify.

Tap for more steps...

Step 4.5.1

Divide each term in $10 x = 8$ by $10$ .

$\frac{10 x}{10} = \frac{8}{10}$

Step 4.5.2

Simplify the left side.

Tap for more steps...

Step 4.5.2.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 4.5.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{8}{10}$

Step 4.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{10}$

Step 4.5.3

Simplify the right side.

Tap for more steps...

Step 4.5.3.1

Cancel the common factor of $8$ and $10$ .

Tap for more steps...

Step 4.5.3.1.1

Factor $2$ out of $8$ .

$x = \frac{2 (4)}{10}$

Step 4.5.3.1.2

Cancel the common factors.

Tap for more steps...

Step 4.5.3.1.2.1

Factor $2$ out of $10$ .

$x = \frac{2 \cdot 4}{2 \cdot 5}$

Step 4.5.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 4}{2 \cdot 5}$

Step 4.5.3.1.2.3

Rewrite the expression.

$x = \frac{4}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{5}$

Decimal Form:

$x = 0.8$