Algebra Examples

$\frac{28}{54} = \frac{2 x + 8}{5 x - 4}$

Step 1

Rewrite the equation as $\frac{2 x + 8}{5 x - 4} = \frac{28}{54}$ .

$\frac{2 x + 8}{5 x - 4} = \frac{28}{54}$

Step 2

Simplify both sides.

Tap for more steps...

Step 2.1

Factor $2$ out of $2 x + 8$ .

Tap for more steps...

Step 2.1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 8}{5 x - 4} = \frac{28}{54}$

Step 2.1.2

Factor $2$ out of $8$ .

$\frac{2 x + 2 \cdot 4}{5 x - 4} = \frac{28}{54}$

Step 2.1.3

Factor $2$ out of $2 x + 2 \cdot 4$ .

$\frac{2 (x + 4)}{5 x - 4} = \frac{28}{54}$

Step 2.2

Cancel the common factor of $28$ and $54$ .

Tap for more steps...

Step 2.2.1

Factor $2$ out of $28$ .

$\frac{2 (x + 4)}{5 x - 4} = \frac{2 (14)}{54}$

Step 2.2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.2.1

Factor $2$ out of $54$ .

$\frac{2 (x + 4)}{5 x - 4} = \frac{2 \cdot 14}{2 \cdot 27}$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 (x + 4)}{5 x - 4} = \frac{2 \cdot 14}{2 \cdot 27}$

Step 2.2.2.3

Rewrite the expression.

$\frac{2 (x + 4)}{5 x - 4} = \frac{14}{27}$

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.

$2 (x + 4) \cdot 27 = (5 x - 4) \cdot 14$

Step 4

Solve the equation for $x$ .

Tap for more steps...

Step 4.1

Simplify $2 (x + 4) \cdot 27$ .

Tap for more steps...

Step 4.1.1

Rewrite.

$0 + 0 + 2 (x + 4) \cdot 27 = (5 x - 4) \cdot 14$

Step 4.1.2

Simplify by adding zeros.

$2 (x + 4) \cdot 27 = (5 x - 4) \cdot 14$

Step 4.1.3

Apply the distributive property.

$(2 x + 2 \cdot 4) \cdot 27 = (5 x - 4) \cdot 14$

Step 4.1.4

Multiply $2$ by $4$ .

$(2 x + 8) \cdot 27 = (5 x - 4) \cdot 14$

Step 4.1.5

Apply the distributive property.

$2 x \cdot 27 + 8 \cdot 27 = (5 x - 4) \cdot 14$

Step 4.1.6

Multiply.

Tap for more steps...

Step 4.1.6.1

Multiply $27$ by $2$ .

$54 x + 8 \cdot 27 = (5 x - 4) \cdot 14$

Step 4.1.6.2

Multiply $8$ by $27$ .

$54 x + 216 = (5 x - 4) \cdot 14$

Step 4.2

Simplify $(5 x - 4) \cdot 14$ .

Tap for more steps...

Step 4.2.1

Apply the distributive property.

$54 x + 216 = 5 x \cdot 14 - 4 \cdot 14$

Step 4.2.2

Multiply.

Tap for more steps...

Step 4.2.2.1

Multiply $14$ by $5$ .

$54 x + 216 = 70 x - 4 \cdot 14$

Step 4.2.2.2

Multiply $- 4$ by $14$ .

$54 x + 216 = 70 x - 56$

Step 4.3

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

Tap for more steps...

Step 4.3.1

Subtract $70 x$ from both sides of the equation.

$54 x + 216 - 70 x = - 56$

Step 4.3.2

Subtract $70 x$ from $54 x$ .

$- 16 x + 216 = - 56$

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 $216$ from both sides of the equation.

$- 16 x = - 56 - 216$

Step 4.4.2

Subtract $216$ from $- 56$ .

$- 16 x = - 272$

Step 4.5

Divide each term in $- 16 x = - 272$ by $- 16$ and simplify.

Tap for more steps...

Step 4.5.1

Divide each term in $- 16 x = - 272$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{- 272}{- 16}$

Step 4.5.2

Simplify the left side.

Tap for more steps...

Step 4.5.2.1

Cancel the common factor of $- 16$ .

Tap for more steps...

Step 4.5.2.1.1

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{- 272}{- 16}$

Step 4.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 272}{- 16}$

Step 4.5.3

Simplify the right side.

Tap for more steps...

Step 4.5.3.1

Divide $- 272$ by $- 16$ .

$x = 17$