Basic Math Examples

$- 4 (\frac{1}{2} y + \frac{5}{4}) - 2 z = 1$

Step 1

Simplify each term.

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Step 1.1

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

$- 4 (\frac{y}{2} + \frac{5}{4}) - 2 z = 1$

Step 1.2

Apply the distributive property.

$- 4 \frac{y}{2} - 4 (\frac{5}{4}) - 2 z = 1$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $- 4$ .

$2 (- 2) \frac{y}{2} - 4 (\frac{5}{4}) - 2 z = 1$

Step 1.3.2

Cancel the common factor.

$2 \cdot - 2 \frac{y}{2} - 4 (\frac{5}{4}) - 2 z = 1$

Step 1.3.3

Rewrite the expression.

$- 2 y - 4 (\frac{5}{4}) - 2 z = 1$

Step 1.4

Cancel the common factor of $4$ .

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Step 1.4.1

Factor $4$ out of $- 4$ .

$- 2 y + 4 (- 1) \frac{5}{4} - 2 z = 1$

Step 1.4.2

Cancel the common factor.

$- 2 y + 4 \cdot - 1 \frac{5}{4} - 2 z = 1$

Step 1.4.3

Rewrite the expression.

$- 2 y - 1 \cdot 5 - 2 z = 1$

Step 1.5

Multiply $- 1$ by $5$ .

$- 2 y - 5 - 2 z = 1$

Step 2

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

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Step 2.1

Add $5$ to both sides of the equation.

$- 2 y - 2 z = 1 + 5$

Step 2.2

Add $2 z$ to both sides of the equation.

$- 2 y = 1 + 5 + 2 z$

Step 2.3

Add $1$ and $5$ .

$- 2 y = 6 + 2 z$

Step 3

Divide each term in $- 2 y = 6 + 2 z$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 y = 6 + 2 z$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{6}{- 2} + \frac{2 z}{- 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{6}{- 2} + \frac{2 z}{- 2}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{- 2} + \frac{2 z}{- 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Divide $6$ by $- 2$ .

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

Step 3.3.1.2

Cancel the common factor of $2$ and $- 2$ .

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Step 3.3.1.2.1

Factor $2$ out of $2 z$ .

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

Step 3.3.1.2.2

Move the negative one from the denominator of $\frac{z}{- 1}$ .

$y = - 3 - 1 \cdot z$

Step 3.3.1.3

Rewrite $- 1 \cdot z$ as $- z$ .

$y = - 3 - z$