Algebra Examples

$6 x + 18 = h (3 x + 9)$

Step 1

Simplify $h (3 x + 9)$ .

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Step 1.1

Rewrite.

$6 x + 18 = 0 + 0 + h (3 x + 9)$

Step 1.2

Simplify by adding zeros.

$6 x + 18 = h (3 x + 9)$

Step 1.3

Apply the distributive property.

$6 x + 18 = h (3 x) + h \cdot 9$

Step 1.4

Reorder.

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Step 1.4.1

Rewrite using the commutative property of multiplication.

$6 x + 18 = 3 h x + h \cdot 9$

Step 1.4.2

Move $9$ to the left of $h$ .

$6 x + 18 = 3 h x + 9 h$

Step 2

Subtract $3 h x$ from both sides of the equation.

$6 x + 18 - 3 h x = 9 h$

Step 3

Subtract $18$ from both sides of the equation.

$6 x - 3 h x = 9 h - 18$

Step 4

Factor $3 x$ out of $6 x - 3 h x$ .

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Step 4.1

Factor $3 x$ out of $6 x$ .

$3 x (2) - 3 h x = 9 h - 18$

Step 4.2

Factor $3 x$ out of $- 3 h x$ .

$3 x (2) + 3 x (- h) = 9 h - 18$

Step 4.3

Factor $3 x$ out of $3 x (2) + 3 x (- h)$ .

$3 x (2 - h) = 9 h - 18$

Step 5

Divide each term in $3 x (2 - h) = 9 h - 18$ by $3 (2 - h)$ and simplify.

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Step 5.1

Divide each term in $3 x (2 - h) = 9 h - 18$ by $3 (2 - h)$ .

$\frac{3 x (2 - h)}{3 (2 - h)} = \frac{9 h}{3 (2 - h)} + \frac{- 18}{3 (2 - h)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 x (2 - h)}{3 (2 - h)} = \frac{9 h}{3 (2 - h)} + \frac{- 18}{3 (2 - h)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{x (2 - h)}{2 - h} = \frac{9 h}{3 (2 - h)} + \frac{- 18}{3 (2 - h)}$

Step 5.2.2

Cancel the common factor of $2 - h$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{x (2 - h)}{2 - h} = \frac{9 h}{3 (2 - h)} + \frac{- 18}{3 (2 - h)}$

Step 5.2.2.2

Divide $x$ by $1$ .

$x = \frac{9 h}{3 (2 - h)} + \frac{- 18}{3 (2 - h)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Cancel the common factor of $9$ and $3$ .

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Step 5.3.1.1.1

Factor $3$ out of $9 h$ .

$x = \frac{3 (3 h)}{3 (2 - h)} + \frac{- 18}{3 (2 - h)}$

Step 5.3.1.1.2

Cancel the common factors.

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Step 5.3.1.1.2.1

Cancel the common factor.

$x = \frac{3 (3 h)}{3 (2 - h)} + \frac{- 18}{3 (2 - h)}$

Step 5.3.1.1.2.2

Rewrite the expression.

$x = \frac{3 h}{2 - h} + \frac{- 18}{3 (2 - h)}$

Step 5.3.1.2

Cancel the common factor of $- 18$ and $3$ .

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Step 5.3.1.2.1

Factor $3$ out of $- 18$ .

$x = \frac{3 h}{2 - h} + \frac{3 \cdot - 6}{3 (2 - h)}$

Step 5.3.1.2.2

Cancel the common factors.

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Step 5.3.1.2.2.1

Cancel the common factor.

$x = \frac{3 h}{2 - h} + \frac{3 \cdot - 6}{3 (2 - h)}$

Step 5.3.1.2.2.2

Rewrite the expression.

$x = \frac{3 h}{2 - h} + \frac{- 6}{2 - h}$

Step 5.3.1.3

Move the negative in front of the fraction.

$x = \frac{3 h}{2 - h} - \frac{6}{2 - h}$

Step 5.3.2

Simplify terms.

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Step 5.3.2.1

Combine the numerators over the common denominator.

$x = \frac{3 h - 6}{2 - h}$

Step 5.3.2.2

Factor $3$ out of $3 h - 6$ .

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Step 5.3.2.2.1

Factor $3$ out of $3 h$ .

$x = \frac{3 (h) - 6}{2 - h}$

Step 5.3.2.2.2

Factor $3$ out of $- 6$ .

$x = \frac{3 h + 3 \cdot - 2}{2 - h}$

Step 5.3.2.2.3

Factor $3$ out of $3 h + 3 \cdot - 2$ .

$x = \frac{3 (h - 2)}{2 - h}$

Step 5.3.2.3

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

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Step 5.3.2.3.1

Factor $- 1$ out of $h$ .

$x = \frac{3 (- 1 (- h) - 2)}{2 - h}$

Step 5.3.2.3.2

Rewrite $- 2$ as $- 1 (2)$ .

$x = \frac{3 (- 1 (- h) - 1 (2))}{2 - h}$

Step 5.3.2.3.3

Factor $- 1$ out of $- 1 (- h) - 1 (2)$ .

$x = \frac{3 (- 1 (- h + 2))}{2 - h}$

Step 5.3.2.3.4

Reorder terms.

$x = \frac{3 (- 1 (- h + 2))}{- h + 2}$

Step 5.3.2.3.5

Cancel the common factor.

$x = \frac{3 (- 1 (- h + 2))}{- h + 2}$

Step 5.3.2.3.6

Divide $3 \cdot (- 1)$ by $1$ .

$x = 3 \cdot (- 1)$

Step 5.3.2.4

Multiply $3$ by $- 1$ .

$x = - 3$