Solve for z (2z+3)/3+(3z-4)/6=(z-2)/2

$\frac{2 z + 3}{3} + \frac{3 z - 4}{6} = \frac{z - 2}{2}$

Move $\frac{z - 2}{2}$ to the left side of the equation by subtracting it from both sides.

$\frac{2 z + 3}{3} + \frac{3 z - 4}{6} - \frac{z - 2}{2} = 0$

Simplify $\frac{2 z + 3}{3} + \frac{3 z - 4}{6} - \frac{z - 2}{2}$ .

Tap for more steps…

Simplify each term.

Tap for more steps…

Split the fraction into multiple fractions.

$\frac{2 z + 3}{3} + \frac{3 z}{6} - \frac{4}{6} - \frac{z - 2}{2} = 0$

Reduce the expression $\frac{3 z}{6}$ by cancelling the common factors.

Tap for more steps…

Factor $3$ out of $3 z$ .

$\frac{2 z + 3}{3} + \frac{3 (z)}{6} - \frac{4}{6} - \frac{z - 2}{2} = 0$

Factor $3$ out of $6$ .

$\frac{2 z + 3}{3} + \frac{3 z}{3 \cdot 2} - \frac{4}{6} - \frac{z - 2}{2} = 0$

Cancel the common factor.

$\frac{2 z + 3}{3} + \frac{3 z}{3 \cdot 2} - \frac{4}{6} - \frac{z - 2}{2} = 0$

Rewrite the expression.

$\frac{2 z + 3}{3} + \frac{z}{2} - \frac{4}{6} - \frac{z - 2}{2} = 0$

Reduce the expression $\frac{4}{6}$ by cancelling the common factors.

Tap for more steps…

Factor $2$ out of $4$ .

$\frac{2 z + 3}{3} + \frac{z}{2} - \frac{2 (2)}{6} - \frac{z - 2}{2} = 0$

Factor $2$ out of $6$ .

$\frac{2 z + 3}{3} + \frac{z}{2} - \frac{2 \cdot 2}{2 \cdot 3} - \frac{z - 2}{2} = 0$

Cancel the common factor.

$\frac{2 z + 3}{3} + \frac{z}{2} - \frac{2 \cdot 2}{2 \cdot 3} - \frac{z - 2}{2} = 0$

Rewrite the expression.

$\frac{2 z + 3}{3} + \frac{z}{2} - \frac{2}{3} - \frac{z - 2}{2} = 0$

Combine fractions with similar denominators.

$\frac{2 z + 3}{3} + \frac{- 2}{3} + \frac{z - (z - 2)}{2} = 0$

Split the fraction $\frac{2 z + 3}{3}$ into two fractions.

$\frac{2 z}{3} + \frac{3}{3} + \frac{- 2}{3} + \frac{z - (z - 2)}{2} = 0$

Reduce the expression $\frac{3}{3}$ by cancelling the common factors.

Tap for more steps…

Cancel the common factor.

$\frac{2 z}{3} + \frac{3}{3} + \frac{- 2}{3} + \frac{z - (z - 2)}{2} = 0$

Rewrite the expression.

$\frac{2 z}{3} + \frac{1}{1} + \frac{- 2}{3} + \frac{z - (z - 2)}{2} = 0$

Simplify the expression.

Tap for more steps…

Divide $1$ by $1$ .

$\frac{2 z}{3} + 1 + \frac{- 2}{3} + \frac{z - (z - 2)}{2} = 0$

Move the negative in front of the fraction.

$\frac{2 z}{3} + 1 - \frac{2}{3} + \frac{z - (z - 2)}{2} = 0$

Apply the distributive property.

$\frac{2 z}{3} + 1 - \frac{2}{3} + \frac{z - z - - 2}{2} = 0$

Multiply $- 1$ by $- 2$ .

$\frac{2 z}{3} + 1 - \frac{2}{3} + \frac{z - z + 2}{2} = 0$

Subtract $z$ from $z$ .

$\frac{2 z}{3} + 1 - \frac{2}{3} + \frac{0 + 2}{2} = 0$

Add $0$ and $2$ .

$\frac{2 z}{3} + 1 - \frac{2}{3} + \frac{2}{2} = 0$

Reduce the expression $\frac{2}{2}$ by cancelling the common factors.

Tap for more steps…

Cancel the common factor.

$\frac{2 z}{3} + 1 - \frac{2}{3} + \frac{2}{2} = 0$

Rewrite the expression.

$\frac{2 z}{3} + 1 - \frac{2}{3} + \frac{1}{1} = 0$

Simplify the expression.

Tap for more steps…

Divide $1$ by $1$ .

$\frac{2 z}{3} + 1 - \frac{2}{3} + 1 = 0$

Add $1$ and $1$ .

$\frac{2 z}{3} + 2 - \frac{2}{3} = 0$

Find the LCD of the terms in the equation.

Tap for more steps…

To find the LCD of a set of numbers $(\frac{2 z}{3}, 2, - \frac{2}{3})$ , find the LCM of the denominators.

$LCM (3, 1, 3)$

Calculate the LCM of first two denominators in the list, $3$ and $1$ .

Tap for more steps…

Find the values of the numerical part of each term. Select the largest one, which in this case is $3$ . Multiply them together to get the current total. In this case, the current total is $3$ .

Current Total = $3$

Check each value in the numerical part of each term against the current total. Since the current total is evenly divisible, return it. That is the least common denominator of the numerical part of the fraction.

$3$

Multiply each term by $3$ and simplify.

Tap for more steps…

Multiply each term in $\frac{2 z}{3} + 2 - \frac{2}{3} = 0$ by $3$ .

$\frac{2 z}{3} \cdot 3 + 2 \cdot 3 - \frac{2}{3} \cdot 3 = 0 \cdot 3$

Simplify $\frac{2 z}{3} \cdot 3 + 2 \cdot 3 - \frac{2}{3} \cdot 3$ .

Tap for more steps…

Simplify each term.

Tap for more steps…

Cancel the common factor of $3$ .

Tap for more steps…

Cancel the common factor.

$\frac{2 z}{3} \cdot 3 + 2 \cdot 3 - \frac{2}{3} \cdot 3 = 0 \cdot 3$

Rewrite the expression.

$2 z + 2 \cdot 3 - \frac{2}{3} \cdot 3 = 0 \cdot 3$

Multiply $2$ by $3$ .

$2 z + 6 - \frac{2}{3} \cdot 3 = 0 \cdot 3$

Cancel the common factor of $3$ .

Tap for more steps…

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$2 z + 6 + \frac{- 2}{3} \cdot 3 = 0 \cdot 3$

Cancel the common factor.

$2 z + 6 + \frac{- 2}{3} \cdot 3 = 0 \cdot 3$

Rewrite the expression.

$2 z + 6 - 2 = 0 \cdot 3$

Subtract $2$ from $6$ .

$2 z + 4 = 0 \cdot 3$

Multiply $0$ by $3$ .

$2 z + 4 = 0$

Subtract $4$ from both sides of the equation.

$2 z = - 4$

Divide each term by $2$ and simplify.

Tap for more steps…

Divide each term in $2 z = - 4$ by $2$ .

$\frac{2 z}{2} = \frac{- 4}{2}$

Cancel the common factor of $2$ .

Tap for more steps…

Cancel the common factor.

$\frac{2 z}{2} = \frac{- 4}{2}$

Divide $z$ by $1$ .

$z = \frac{- 4}{2}$

Divide $- 4$ by $2$ .

$z = - 2$

Solve for z (2z+3)/3+(3z-4)/6=(z-2)/2

Solving MATH problems