Basic Math Examples

$3 (2 y - 1) = 5 (2 - z)$

Step 1

Divide each term in $3 (2 y - 1) = 5 (2 - z)$ by $3$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $3 (2 y - 1) = 5 (2 - z)$ by $3$ .

$\frac{3 (2 y - 1)}{3} = \frac{5 (2 - z)}{3}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{3 (2 y - 1)}{3} = \frac{5 (2 - z)}{3}$

Step 1.2.1.2

Divide $2 y - 1$ by $1$ .

$2 y - 1 = \frac{5 (2 - z)}{3}$

Step 2

Add $1$ to both sides of the equation.

$2 y = \frac{5 (2 - z)}{3} + 1$

Step 3

Divide each term in $2 y = \frac{5 (2 - z)}{3} + 1$ by $2$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $2 y = \frac{5 (2 - z)}{3} + 1$ by $2$ .

$\frac{2 y}{2} = \frac{\frac{5 (2 - z)}{3}}{2} + \frac{1}{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{\frac{5 (2 - z)}{3}}{2} + \frac{1}{2}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{5 (2 - z)}{3}}{2} + \frac{1}{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Simplify terms.

Tap for more steps...

Step 3.3.1.1

Combine the numerators over the common denominator.

$y = \frac{\frac{5 (2 - z)}{3} + 1}{2}$

Step 3.3.1.2

Write $1$ as a fraction with a common denominator.

$y = \frac{\frac{5 (2 - z)}{3} + \frac{3}{3}}{2}$

Step 3.3.1.3

Combine the numerators over the common denominator.

$y = \frac{\frac{5 (2 - z) + 3}{3}}{2}$

Step 3.3.2

Simplify the numerator.

Tap for more steps...

Step 3.3.2.1

Apply the distributive property.

$y = \frac{\frac{5 \cdot 2 + 5 (- z) + 3}{3}}{2}$

Step 3.3.2.2

Multiply $5$ by $2$ .

$y = \frac{\frac{10 + 5 (- z) + 3}{3}}{2}$

Step 3.3.2.3

Multiply $- 1$ by $5$ .

$y = \frac{\frac{10 - 5 z + 3}{3}}{2}$

Step 3.3.2.4

Add $10$ and $3$ .

$y = \frac{\frac{- 5 z + 13}{3}}{2}$

Step 3.3.3

Simplify with factoring out.

Tap for more steps...

Step 3.3.3.1

Factor $- 1$ out of $- 5 z$ .

$y = \frac{\frac{- (5 z) + 13}{3}}{2}$

Step 3.3.3.2

Rewrite $13$ as $- 1 (- 13)$ .

$y = \frac{\frac{- (5 z) - 1 (- 13)}{3}}{2}$

Step 3.3.3.3

Factor $- 1$ out of $- (5 z) - 1 (- 13)$ .

$y = \frac{\frac{- (5 z - 13)}{3}}{2}$

Step 3.3.3.4

Simplify the expression.

Tap for more steps...

Step 3.3.3.4.1

Rewrite $- (5 z - 13)$ as $- 1 (5 z - 13)$ .

$y = \frac{\frac{- 1 (5 z - 13)}{3}}{2}$

Step 3.3.3.4.2

Move the negative in front of the fraction.

$y = \frac{- \frac{5 z - 13}{3}}{2}$

Step 3.3.4

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{5 z - 13}{3} \cdot \frac{1}{2}$

Step 3.3.5

Multiply $- \frac{5 z - 13}{3} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 3.3.5.1

Multiply $\frac{1}{2}$ by $\frac{5 z - 13}{3}$ .

$y = - \frac{5 z - 13}{2 \cdot 3}$

Step 3.3.5.2

Multiply $2$ by $3$ .

$y = - \frac{5 z - 13}{6}$