Algebra Examples

$5 (x - a) = 3 (x + b)$

Step 1

Simplify $5 (x - a)$ .

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Step 1.1

Rewrite.

$0 + 0 + 5 (x - a) = 3 (x + b)$

Step 1.2

Simplify by adding zeros.

$5 (x - a) = 3 (x + b)$

Step 1.3

Apply the distributive property.

$5 x + 5 (- a) = 3 (x + b)$

Step 1.4

Multiply $- 1$ by $5$ .

$5 x - 5 a = 3 (x + b)$

Step 2

Apply the distributive property.

$5 x - 5 a = 3 x + 3 b$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

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

$5 x - 5 a - 3 x = 3 b$

Step 3.2

Subtract $3 x$ from $5 x$ .

$- 5 a + 2 x = 3 b$

Step 4

Add $5 a$ to both sides of the equation.

$2 x = 3 b + 5 a$

Step 5

Divide each term in $2 x = 3 b + 5 a$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = 3 b + 5 a$ by $2$ .

$\frac{2 x}{2} = \frac{3 b}{2} + \frac{5 a}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3 b}{2} + \frac{5 a}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{3 b}{2} + \frac{5 a}{2}$