Basic Math Examples

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

Step 1

Multiply both sides by $4$ .

$(\frac{z + 3}{6} + 1) \cdot 4 = \frac{2 z + 7}{4} \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{z + 3}{6} + 1) \cdot 4$ .

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Step 2.1.1.1

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

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

Step 2.1.1.2

Combine the numerators over the common denominator.

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

Step 2.1.1.3

Add $3$ and $6$ .

$\frac{z + 9}{6} \cdot 4 = \frac{2 z + 7}{4} \cdot 4$

Step 2.1.1.4

Cancel the common factor of $2$ .

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Step 2.1.1.4.1

Factor $2$ out of $6$ .

$\frac{z + 9}{2 (3)} \cdot 4 = \frac{2 z + 7}{4} \cdot 4$

Step 2.1.1.4.2

Factor $2$ out of $4$ .

$\frac{z + 9}{2 \cdot 3} \cdot (2 \cdot 2) = \frac{2 z + 7}{4} \cdot 4$

Step 2.1.1.4.3

Cancel the common factor.

$\frac{z + 9}{2 \cdot 3} \cdot (2 \cdot 2) = \frac{2 z + 7}{4} \cdot 4$

Step 2.1.1.4.4

Rewrite the expression.

$\frac{z + 9}{3} \cdot 2 = \frac{2 z + 7}{4} \cdot 4$

Step 2.1.1.5

Combine $\frac{z + 9}{3}$ and $2$ .

$\frac{(z + 9) \cdot 2}{3} = \frac{2 z + 7}{4} \cdot 4$

Step 2.1.1.6

Move $2$ to the left of $z + 9$ .

$\frac{2 (z + 9)}{3} = \frac{2 z + 7}{4} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 (z + 9)}{3} = \frac{2 z + 7}{4} \cdot 4$

Step 2.2.1.2

Rewrite the expression.

$\frac{2 (z + 9)}{3} = 2 z + 7$

Step 3

Solve for $z$ .

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Step 3.1

Multiply both sides by $3$ .

$\frac{2 (z + 9)}{3} \cdot 3 = (2 z + 7) \cdot 3$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $\frac{2 (z + 9)}{3} \cdot 3$ .

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Step 3.2.1.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{2 (z + 9)}{3} \cdot 3 = (2 z + 7) \cdot 3$

Step 3.2.1.1.1.2

Rewrite the expression.

$2 (z + 9) = (2 z + 7) \cdot 3$

Step 3.2.1.1.2

Apply the distributive property.

$2 z + 2 \cdot 9 = (2 z + 7) \cdot 3$

Step 3.2.1.1.3

Multiply $2$ by $9$ .

$2 z + 18 = (2 z + 7) \cdot 3$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(2 z + 7) \cdot 3$ .

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Step 3.2.2.1.1

Apply the distributive property.

$2 z + 18 = 2 z \cdot 3 + 7 \cdot 3$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $3$ by $2$ .

$2 z + 18 = 6 z + 7 \cdot 3$

Step 3.2.2.1.2.2

Multiply $7$ by $3$ .

$2 z + 18 = 6 z + 21$

Step 3.3

Solve for $z$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $6 z$ from both sides of the equation.

$2 z + 18 - 6 z = 21$

Step 3.3.1.2

Subtract $6 z$ from $2 z$ .

$- 4 z + 18 = 21$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $18$ from both sides of the equation.

$- 4 z = 21 - 18$

Step 3.3.2.2

Subtract $18$ from $21$ .

$- 4 z = 3$

Step 3.3.3

Divide each term in $- 4 z = 3$ by $- 4$ and simplify.

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Step 3.3.3.1

Divide each term in $- 4 z = 3$ by $- 4$ .

$\frac{- 4 z}{- 4} = \frac{3}{- 4}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $- 4$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 4 z}{- 4} = \frac{3}{- 4}$

Step 3.3.3.2.1.2

Divide $z$ by $1$ .

$z = \frac{3}{- 4}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Move the negative in front of the fraction.

$z = - \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{3}{4}$

Decimal Form:

$z = - 0.75$