Evaluate (2a+5)/5=(3a+11)/4

$\frac{2 a + 5}{5} = \frac{3 a + 11}{4}$

Step 1

Multiply both sides by $5$ .

$\frac{2 a + 5}{5} \cdot 5 = \frac{3 a + 11}{4} \cdot 5$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 a + 5}{5} \cdot 5 = \frac{3 a + 11}{4} \cdot 5$

Rewrite the expression.

$2 a + 5 = \frac{3 a + 11}{4} \cdot 5$

Simplify the right side.

Simplify $\frac{3 a + 11}{4} \cdot 5$ .

Combine $\frac{3 a + 11}{4}$ and $5$ .

$2 a + 5 = \frac{(3 a + 11) \cdot 5}{4}$

Move $5$ to the left of $3 a + 11$ .

$2 a + 5 = \frac{5 (3 a + 11)}{4}$

Step 3

Solve for $a$ .

Multiply both sides by $4$ .

$(2 a + 5) \cdot 4 = \frac{5 (3 a + 11)}{4} \cdot 4$

Simplify.

Simplify the left side.

Simplify $(2 a + 5) \cdot 4$ .

Apply the distributive property.

$2 a \cdot 4 + 5 \cdot 4 = \frac{5 (3 a + 11)}{4} \cdot 4$

Multiply.

Multiply $4$ by $2$ .

$8 a + 5 \cdot 4 = \frac{5 (3 a + 11)}{4} \cdot 4$

Multiply $5$ by $4$ .

$8 a + 20 = \frac{5 (3 a + 11)}{4} \cdot 4$

Simplify the right side.

Simplify $\frac{5 (3 a + 11)}{4} \cdot 4$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$8 a + 20 = \frac{5 (3 a + 11)}{4} \cdot 4$

Rewrite the expression.

$8 a + 20 = 5 (3 a + 11)$

Apply the distributive property.

$8 a + 20 = 5 (3 a) + 5 \cdot 11$

Multiply.

Multiply $3$ by $5$ .

$8 a + 20 = 15 a + 5 \cdot 11$

Multiply $5$ by $11$ .

$8 a + 20 = 15 a + 55$

Solve for $a$ .

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

Subtract $15 a$ from both sides of the equation.

$8 a + 20 - 15 a = 55$

Subtract $15 a$ from $8 a$ .

$- 7 a + 20 = 55$

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

Subtract $20$ from both sides of the equation.

$- 7 a = 55 - 20$

Subtract $20$ from $55$ .

$- 7 a = 35$

Divide each term in $- 7 a = 35$ by $- 7$ and simplify.

Divide each term in $- 7 a = 35$ by $- 7$ .

$\frac{- 7 a}{- 7} = \frac{35}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 a}{- 7} = \frac{35}{- 7}$

Divide $a$ by $1$ .

$a = \frac{35}{- 7}$

Simplify the right side.

Divide $35$ by $- 7$ .

$a = - 5$

Evaluate (2a+5)/5=(3a+11)/4

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