Algebra Examples

$a g (\frac{3 L}{2} - x) = A g x$

Step 1

Simplify $a g (\frac{3 L}{2} - x)$ .

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Step 1.1

Rewrite.

$0 + 0 + a g (\frac{3 L}{2} - x) = A g x$

Step 1.2

Simplify by adding zeros.

$a g (\frac{3 L}{2} - x) = A g x$

Step 1.3

Apply the distributive property.

$a g \frac{3 L}{2} + a g (- x) = A g x$

Step 1.4

Multiply $a g \frac{3 L}{2}$ .

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Step 1.4.1

Combine $a$ and $\frac{3 L}{2}$ .

$g \frac{a (3 L)}{2} + a g (- x) = A g x$

Step 1.4.2

Combine $g$ and $\frac{a (3 L)}{2}$ .

$\frac{g (a (3 L))}{2} + a g (- x) = A g x$

Step 1.5

Rewrite using the commutative property of multiplication.

$\frac{g (a (3 L))}{2} - a g x = A g x$

Step 1.6

Move $3$ to the left of $g a$ .

$\frac{3 g a L}{2} - a g x = A g x$

Step 2

Subtract $A g x$ from both sides of the equation.

$\frac{3 g a L}{2} - a g x - A g x = 0$

Step 3

Subtract $\frac{3 g a L}{2}$ from both sides of the equation.

$- a g x - A g x = - \frac{3 g a L}{2}$

Step 4

Factor $g x$ out of $- a g x - A g x$ .

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Step 4.1

Factor $g x$ out of $- a g x$ .

$g x (- a) - A g x = - \frac{3 g a L}{2}$

Step 4.2

Factor $g x$ out of $- A g x$ .

$g x (- a) + g x (- A) = - \frac{3 g a L}{2}$

Step 4.3

Factor $g x$ out of $g x (- a) + g x (- A)$ .

$g x (- a - A) = - \frac{3 g a L}{2}$

Step 5

Divide each term in $g x (- a - A) = - \frac{3 g a L}{2}$ by $g (- a - A)$ and simplify.

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Step 5.1

Divide each term in $g x (- a - A) = - \frac{3 g a L}{2}$ by $g (- a - A)$ .

$\frac{g x (- a - A)}{g (- a - A)} = \frac{- \frac{3 g a L}{2}}{g (- a - A)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $g$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{g x (- a - A)}{g (- a - A)} = \frac{- \frac{3 g a L}{2}}{g (- a - A)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{x (- a - A)}{- a - A} = \frac{- \frac{3 g a L}{2}}{g (- a - A)}$

Step 5.2.2

Cancel the common factor of $- a - A$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{x (- a - A)}{- a - A} = \frac{- \frac{3 g a L}{2}}{g (- a - A)}$

Step 5.2.2.2

Divide $x$ by $1$ .

$x = \frac{- \frac{3 g a L}{2}}{g (- a - A)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{3 g a L}{2} \cdot \frac{1}{g (- a - A)}$

Step 5.3.2

Cancel the common factor of $g$ .

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Step 5.3.2.1

Move the leading negative in $- \frac{3 g a L}{2}$ into the numerator.

$x = \frac{- 3 g a L}{2} \cdot \frac{1}{g (- a - A)}$

Step 5.3.2.2

Factor $g$ out of $- 3 g a L$ .

$x = \frac{g (- 3 a L)}{2} \cdot \frac{1}{g (- a - A)}$

Step 5.3.2.3

Cancel the common factor.

$x = \frac{g (- 3 a L)}{2} \cdot \frac{1}{g (- a - A)}$

Step 5.3.2.4

Rewrite the expression.

$x = \frac{- 3 a L}{2} \cdot \frac{1}{- a - A}$

Step 5.3.3

Multiply $\frac{- 3 a L}{2}$ by $\frac{1}{- a - A}$ .

$x = \frac{- 3 a L}{2 (- a - A)}$

Step 5.3.4

Move the negative in front of the fraction.

$x = - \frac{3 a L}{2 (- a - A)}$

Step 5.3.5

Factor $- 1$ out of $- a$ .

$x = - \frac{3 a L}{2 (- (a) - A)}$

Step 5.3.6

Factor $- 1$ out of $- A$ .

$x = - \frac{3 a L}{2 (- (a) - (A))}$

Step 5.3.7

Factor $- 1$ out of $- (a) - (A)$ .

$x = - \frac{3 a L}{2 (- (a + A))}$

Step 5.3.8

Simplify the expression.

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Step 5.3.8.1

Rewrite $- (a + A)$ as $- 1 (a + A)$ .

$x = - \frac{3 a L}{2 (- 1 (a + A))}$

Step 5.3.8.2

Move the negative in front of the fraction.

$x = - - \frac{3 a L}{2 (a + A)}$

Step 5.3.8.3

Multiply $- 1$ by $- 1$ .

$x = 1 \frac{3 a L}{2 (a + A)}$

Step 5.3.8.4

Multiply $\frac{3 a L}{2 (a + A)}$ by $1$ .

$x = \frac{3 a L}{2 (a + A)}$