Basic Math Examples

$\frac{1}{2} z - 5 + \frac{2}{3} z = \frac{7}{6} z + 4$

Step 1

Simplify $\frac{1}{2} z - 5 + \frac{2}{3} z$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{2}$ and $z$ .

$\frac{z}{2} - 5 + \frac{2}{3} z = \frac{7}{6} z + 4$

Step 1.1.2

Combine $\frac{2}{3}$ and $z$ .

$\frac{z}{2} - 5 + \frac{2 z}{3} = \frac{7}{6} z + 4$

Step 1.2

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

$\frac{z}{2} \cdot \frac{3}{3} + \frac{2 z}{3} - 5 = \frac{7}{6} z + 4$

Step 1.3

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

$\frac{z}{2} \cdot \frac{3}{3} + \frac{2 z}{3} \cdot \frac{2}{2} - 5 = \frac{7}{6} z + 4$

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{z}{2}$ by $\frac{3}{3}$ .

$\frac{z \cdot 3}{2 \cdot 3} + \frac{2 z}{3} \cdot \frac{2}{2} - 5 = \frac{7}{6} z + 4$

Step 1.4.2

Multiply $2$ by $3$ .

$\frac{z \cdot 3}{6} + \frac{2 z}{3} \cdot \frac{2}{2} - 5 = \frac{7}{6} z + 4$

Step 1.4.3

Multiply $\frac{2 z}{3}$ by $\frac{2}{2}$ .

$\frac{z \cdot 3}{6} + \frac{2 z \cdot 2}{3 \cdot 2} - 5 = \frac{7}{6} z + 4$

Step 1.4.4

Multiply $3$ by $2$ .

$\frac{z \cdot 3}{6} + \frac{2 z \cdot 2}{6} - 5 = \frac{7}{6} z + 4$

Step 1.5

Combine the numerators over the common denominator.

$\frac{z \cdot 3 + 2 z \cdot 2}{6} - 5 = \frac{7}{6} z + 4$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $z$ out of $z \cdot 3 + 2 z \cdot 2$ .

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Step 1.6.1.1.1

Factor $z$ out of $z \cdot 3$ .

$\frac{z (3) + 2 z \cdot 2}{6} - 5 = \frac{7}{6} z + 4$

Step 1.6.1.1.2

Factor $z$ out of $2 z \cdot 2$ .

$\frac{z (3) + z (2 \cdot 2)}{6} - 5 = \frac{7}{6} z + 4$

Step 1.6.1.1.3

Factor $z$ out of $z (3) + z (2 \cdot 2)$ .

$\frac{z (3 + 2 \cdot 2)}{6} - 5 = \frac{7}{6} z + 4$

Step 1.6.1.2

Multiply $2$ by $2$ .

$\frac{z (3 + 4)}{6} - 5 = \frac{7}{6} z + 4$

Step 1.6.1.3

Add $3$ and $4$ .

$\frac{z \cdot 7}{6} - 5 = \frac{7}{6} z + 4$

Step 1.6.2

Move $7$ to the left of $z$ .

$\frac{7 z}{6} - 5 = \frac{7}{6} z + 4$

Step 2

Combine $\frac{7}{6}$ and $z$ .

$\frac{7 z}{6} - 5 = \frac{7 z}{6} + 4$

Step 3

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

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Step 3.1

Subtract $\frac{7 z}{6}$ from both sides of the equation.

$\frac{7 z}{6} - 5 - \frac{7 z}{6} = 4$

Step 3.2

Combine the opposite terms in $\frac{7 z}{6} - 5 - \frac{7 z}{6}$ .

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Step 3.2.1

Subtract $\frac{7 z}{6}$ from $\frac{7 z}{6}$ .

$0 - 5 = 4$

Step 3.2.2

Subtract $5$ from $0$ .

$- 5 = 4$

Step 4

Since $- 5 \neq 4$ , there are no solutions.

No solution