Algebra Examples

$35 x - 56 = g (- 5 x + 8)$

Step 1

Simplify $g (- 5 x + 8)$ .

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Step 1.1

Rewrite.

$35 x - 56 = 0 + 0 + g (- 5 x + 8)$

Step 1.2

Simplify by adding zeros.

$35 x - 56 = g (- 5 x + 8)$

Step 1.3

Apply the distributive property.

$35 x - 56 = g (- 5 x) + g \cdot 8$

Step 1.4

Reorder.

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Step 1.4.1

Rewrite using the commutative property of multiplication.

$35 x - 56 = - 5 g x + g \cdot 8$

Step 1.4.2

Move $8$ to the left of $g$ .

$35 x - 56 = - 5 g x + 8 g$

Step 2

Add $5 g x$ to both sides of the equation.

$35 x - 56 + 5 g x = 8 g$

Step 3

Add $56$ to both sides of the equation.

$35 x + 5 g x = 8 g + 56$

Step 4

Factor $5 x$ out of $35 x + 5 g x$ .

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Step 4.1

Factor $5 x$ out of $35 x$ .

$5 x (7) + 5 g x = 8 g + 56$

Step 4.2

Factor $5 x$ out of $5 g x$ .

$5 x (7) + 5 x (g) = 8 g + 56$

Step 4.3

Factor $5 x$ out of $5 x (7) + 5 x (g)$ .

$5 x (7 + g) = 8 g + 56$

Step 5

Divide each term in $5 x (7 + g) = 8 g + 56$ by $5 (7 + g)$ and simplify.

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Step 5.1

Divide each term in $5 x (7 + g) = 8 g + 56$ by $5 (7 + g)$ .

$\frac{5 x (7 + g)}{5 (7 + g)} = \frac{8 g}{5 (7 + g)} + \frac{56}{5 (7 + g)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 x (7 + g)}{5 (7 + g)} = \frac{8 g}{5 (7 + g)} + \frac{56}{5 (7 + g)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{x (7 + g)}{7 + g} = \frac{8 g}{5 (7 + g)} + \frac{56}{5 (7 + g)}$

Step 5.2.2

Cancel the common factor of $7 + g$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{x (7 + g)}{7 + g} = \frac{8 g}{5 (7 + g)} + \frac{56}{5 (7 + g)}$

Step 5.2.2.2

Divide $x$ by $1$ .

$x = \frac{8 g}{5 (7 + g)} + \frac{56}{5 (7 + g)}$