Algebra Examples

- \frac{5}{6} (42 x + 18 y) - (2 y - x)

$- \frac{5}{6} (42 x + 18 y) - (2 y - x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

- \frac{5}{6} (42 x) - \frac{5}{6} (18 y) - (2 y - x)

$- \frac{5}{6} (42 x) - \frac{5}{6} (18 y) - (2 y - x)$

Step 1.2

Cancel the common factor of

6

$6$ .

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Step 1.2.1

Move the leading negative in

- \frac{5}{6}

$- \frac{5}{6}$ into the numerator.

\frac{- 5}{6} (42 x) - \frac{5}{6} (18 y) - (2 y - x)

$\frac{- 5}{6} (42 x) - \frac{5}{6} (18 y) - (2 y - x)$

Step 1.2.2

Factor

6

$6$ out of

42 x

$42 x$ .

\frac{- 5}{6} (6 (7 x)) - \frac{5}{6} (18 y) - (2 y - x)

$\frac{- 5}{6} (6 (7 x)) - \frac{5}{6} (18 y) - (2 y - x)$

Step 1.2.3

Cancel the common factor.

$\frac{- 5}{6} (6 (7 x)) - \frac{5}{6} (18 y) - (2 y - x)$

Step 1.2.4

Rewrite the expression.

$- 5 (7 x) - \frac{5}{6} (18 y) - (2 y - x)$

Step 1.3

Multiply

$7$ by

$- 5$ .

$- 35 x - \frac{5}{6} (18 y) - (2 y - x)$

Step 1.4

Cancel the common factor of

$6$ .

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Step 1.4.1

Move the leading negative in

$- \frac{5}{6}$ into the numerator.

$- 35 x + \frac{- 5}{6} (18 y) - (2 y - x)$

Step 1.4.2

Factor

$6$ out of

$18 y$ .

$- 35 x + \frac{- 5}{6} (6 (3 y)) - (2 y - x)$

Step 1.4.3

Cancel the common factor.

$- 35 x + \frac{- 5}{6} (6 (3 y)) - (2 y - x)$

Step 1.4.4

Rewrite the expression.

$- 35 x - 5 (3 y) - (2 y - x)$

Step 1.5

Multiply

$3$ by

$- 5$ .

$- 35 x - 15 y - (2 y - x)$

Step 1.6

Apply the distributive property.

$- 35 x - 15 y - (2 y) - - x$

Step 1.7

Multiply

$2$ by

$- 1$ .

$- 35 x - 15 y - 2 y - - x$

Step 1.8

Multiply

$- - x$ .

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Step 1.8.1

Multiply

$- 1$ by

$- 1$ .

$- 35 x - 15 y - 2 y + 1 x$

Step 1.8.2

Multiply

$x$ by

$1$ .

$- 35 x - 15 y - 2 y + x$

Step 2

Simplify by adding terms.

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Step 2.1

Add

$- 35 x$ and

$x$ .

$- 34 x - 15 y - 2 y$

Step 2.2

Subtract

$2 y$ from

$- 15 y$ .

$- 34 x - 17 y$