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

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

Step 1

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

To write $\frac{2 Z - 3}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

To write $\frac{Z + 2}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 Z - 3}{6}$ by $\frac{2}{2}$ .

$\frac{(2 Z - 3) \cdot 2}{6 \cdot 2} + \frac{Z + 2}{4} \cdot \frac{3}{3} = 4$

Multiply $6$ by $2$ .

$\frac{(2 Z - 3) \cdot 2}{12} + \frac{Z + 2}{4} \cdot \frac{3}{3} = 4$

Multiply $\frac{Z + 2}{4}$ by $\frac{3}{3}$ .

$\frac{(2 Z - 3) \cdot 2}{12} + \frac{(Z + 2) \cdot 3}{4 \cdot 3} = 4$

Multiply $4$ by $3$ .

$\frac{(2 Z - 3) \cdot 2}{12} + \frac{(Z + 2) \cdot 3}{12} = 4$

Combine the numerators over the common denominator.

$\frac{(2 Z - 3) \cdot 2 + (Z + 2) \cdot 3}{12} = 4$

Simplify the numerator.

Apply the distributive property.

$\frac{2 Z \cdot 2 - 3 \cdot 2 + (Z + 2) \cdot 3}{12} = 4$

Multiply $2$ by $2$ .

$\frac{4 Z - 3 \cdot 2 + (Z + 2) \cdot 3}{12} = 4$

Multiply $- 3$ by $2$ .

$\frac{4 Z - 6 + (Z + 2) \cdot 3}{12} = 4$

Apply the distributive property.

$\frac{4 Z - 6 + Z \cdot 3 + 2 \cdot 3}{12} = 4$

Move $3$ to the left of $Z$ .

$\frac{4 Z - 6 + 3 \cdot Z + 2 \cdot 3}{12} = 4$

Multiply $2$ by $3$ .

$\frac{4 Z - 6 + 3 \cdot Z + 6}{12} = 4$

Add $4 Z$ and $3 Z$ .

$\frac{7 Z - 6 + 6}{12} = 4$

Add $- 6$ and $6$ .

$\frac{7 Z + 0}{12} = 4$

Add $7 Z$ and $0$ .

$\frac{7 Z}{12} = 4$

Step 2

Multiply both sides of the equation by $\frac{12}{7}$ .

$\frac{12}{7} \cdot \frac{7 Z}{12} = \frac{12}{7} \cdot 4$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{7} \cdot \frac{7 Z}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{7} \cdot \frac{7 Z}{12} = \frac{12}{7} \cdot 4$

Rewrite the expression.

$\frac{1}{7} (7 Z) = \frac{12}{7} \cdot 4$

Cancel the common factor of $7$ .

Factor $7$ out of $7 Z$ .

$\frac{1}{7} (7 (Z)) = \frac{12}{7} \cdot 4$

Cancel the common factor.

$\frac{1}{7} (7 Z) = \frac{12}{7} \cdot 4$

Rewrite the expression.

$Z = \frac{12}{7} \cdot 4$

Simplify the right side.

Multiply $\frac{12}{7} \cdot 4$ .

Combine $\frac{12}{7}$ and $4$ .

$Z = \frac{12 \cdot 4}{7}$

Multiply $12$ by $4$ .

$Z = \frac{48}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$Z = \frac{48}{7}$

Decimal Form:

$Z = 6.\overline{857142}$

Mixed Number Form:

$Z = 6 \frac{6}{7}$

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

Related Questions