Precalculus Examples

$a - 2 (b - 3 (c - x)) = 6$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$a - 2 (b - 3 c - 3 (- x)) = 6$

Step 1.1.2

Multiply $- 1$ by $- 3$ .

$a - 2 (b - 3 c + 3 x) = 6$

Step 1.2

Apply the distributive property.

$a - 2 b - 2 (- 3 c) - 2 (3 x) = 6$

Step 1.3

Simplify.

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Step 1.3.1

Multiply $- 3$ by $- 2$ .

$a - 2 b + 6 c - 2 (3 x) = 6$

Step 1.3.2

Multiply $3$ by $- 2$ .

$a - 2 b + 6 c - 6 x = 6$

Step 2

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

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Step 2.1

Subtract $a$ from both sides of the equation.

$- 2 b + 6 c - 6 x = 6 - a$

Step 2.2

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

$6 c - 6 x = 6 - a + 2 b$

Step 2.3

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

$- 6 x = 6 - a + 2 b - 6 c$

Step 3

Divide each term in $- 6 x = 6 - a + 2 b - 6 c$ by $- 6$ and simplify.

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Step 3.1

Divide each term in $- 6 x = 6 - a + 2 b - 6 c$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{6}{- 6} + \frac{- a}{- 6} + \frac{2 b}{- 6} + \frac{- 6 c}{- 6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{6}{- 6} + \frac{- a}{- 6} + \frac{2 b}{- 6} + \frac{- 6 c}{- 6}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{- 6} + \frac{- a}{- 6} + \frac{2 b}{- 6} + \frac{- 6 c}{- 6}$

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 $- 6$ .

$x = - 1 + \frac{- a}{- 6} + \frac{2 b}{- 6} + \frac{- 6 c}{- 6}$

Step 3.3.1.2

Dividing two negative values results in a positive value.

$x = - 1 + \frac{a}{6} + \frac{2 b}{- 6} + \frac{- 6 c}{- 6}$

Step 3.3.1.3

Cancel the common factor of $2$ and $- 6$ .

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Step 3.3.1.3.1

Factor $2$ out of $2 b$ .

$x = - 1 + \frac{a}{6} + \frac{2 (b)}{- 6} + \frac{- 6 c}{- 6}$

Step 3.3.1.3.2

Cancel the common factors.

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Step 3.3.1.3.2.1

Factor $2$ out of $- 6$ .

$x = - 1 + \frac{a}{6} + \frac{2 b}{2 \cdot - 3} + \frac{- 6 c}{- 6}$

Step 3.3.1.3.2.2

Cancel the common factor.

$x = - 1 + \frac{a}{6} + \frac{2 b}{2 \cdot - 3} + \frac{- 6 c}{- 6}$

Step 3.3.1.3.2.3

Rewrite the expression.

$x = - 1 + \frac{a}{6} + \frac{b}{- 3} + \frac{- 6 c}{- 6}$

Step 3.3.1.4

Move the negative in front of the fraction.

$x = - 1 + \frac{a}{6} - \frac{b}{3} + \frac{- 6 c}{- 6}$

Step 3.3.1.5

Cancel the common factor of $- 6$ .

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Step 3.3.1.5.1

Cancel the common factor.

$x = - 1 + \frac{a}{6} - \frac{b}{3} + \frac{- 6 c}{- 6}$

Step 3.3.1.5.2

Divide $c$ by $1$ .

$x = - 1 + \frac{a}{6} - \frac{b}{3} + c$