Basic Math Examples

5 x + 7 = - y - 4 z

$5 x + 7 = - y - 4 z$

Step 1

Rewrite the equation as

- y - 4 z = 5 x + 7

$- y - 4 z = 5 x + 7$ .

- y - 4 z = 5 x + 7

$- y - 4 z = 5 x + 7$

Step 2

Add

4 z

$4 z$ to both sides of the equation.

- y = 5 x + 7 + 4 z

$- y = 5 x + 7 + 4 z$

Step 3

Divide each term in

- y = 5 x + 7 + 4 z

$- y = 5 x + 7 + 4 z$ by

- 1

$- 1$ and simplify.

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Step 3.1

Divide each term in

- y = 5 x + 7 + 4 z

$- y = 5 x + 7 + 4 z$ by

- 1

$- 1$ .

\frac{- y}{- 1} = \frac{5 x}{- 1} + \frac{7}{- 1} + \frac{4 z}{- 1}

$\frac{- y}{- 1} = \frac{5 x}{- 1} + \frac{7}{- 1} + \frac{4 z}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

\frac{y}{1} = \frac{5 x}{- 1} + \frac{7}{- 1} + \frac{4 z}{- 1}

$\frac{y}{1} = \frac{5 x}{- 1} + \frac{7}{- 1} + \frac{4 z}{- 1}$

Step 3.2.2

Divide

y

$y$ by

1

$1$ .

y = \frac{5 x}{- 1} + \frac{7}{- 1} + \frac{4 z}{- 1}

$y = \frac{5 x}{- 1} + \frac{7}{- 1} + \frac{4 z}{- 1}$

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

Move the negative one from the denominator of

$\frac{5 x}{- 1}$ .

$y = - 1 \cdot (5 x) + \frac{7}{- 1} + \frac{4 z}{- 1}$

Step 3.3.1.2

Rewrite

$- 1 \cdot (5 x)$ as

$- (5 x)$ .

$y = - (5 x) + \frac{7}{- 1} + \frac{4 z}{- 1}$

Step 3.3.1.3

Multiply

$5$ by

$- 1$ .

$y = - 5 x + \frac{7}{- 1} + \frac{4 z}{- 1}$

Step 3.3.1.4

Divide

$7$ by

$- 1$ .

$y = - 5 x - 7 + \frac{4 z}{- 1}$

Step 3.3.1.5

Move the negative one from the denominator of

$\frac{4 z}{- 1}$ .

$y = - 5 x - 7 - 1 \cdot (4 z)$

Step 3.3.1.6

Rewrite

$- 1 \cdot (4 z)$ as

$- (4 z)$ .

$y = - 5 x - 7 - (4 z)$

Step 3.3.1.7

Multiply

$4$ by

$- 1$ .

$y = - 5 x - 7 - 4 z$