Algebra Examples

$5 x - (x + 3) = \frac{1}{3} (9 x + 18) - 5$

Step 1

Simplify $5 x - (x + 3)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 x - x - 1 \cdot 3 = \frac{1}{3} \cdot (9 x + 18) - 5$

Step 1.1.2

Multiply $- 1$ by $3$ .

$5 x - x - 3 = \frac{1}{3} \cdot (9 x + 18) - 5$

Step 1.2

Subtract $x$ from $5 x$ .

$4 x - 3 = \frac{1}{3} \cdot (9 x + 18) - 5$

Step 2

Simplify $\frac{1}{3} \cdot (9 x + 18) - 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 x - 3 = \frac{1}{3} (9 x) + \frac{1}{3} \cdot 18 - 5$

Step 2.1.2

Cancel the common factor of $3$ .

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Step 2.1.2.1

Factor $3$ out of $9 x$ .

$4 x - 3 = \frac{1}{3} (3 (3 x)) + \frac{1}{3} \cdot 18 - 5$

Step 2.1.2.2

Cancel the common factor.

$4 x - 3 = \frac{1}{3} (3 (3 x)) + \frac{1}{3} \cdot 18 - 5$

Step 2.1.2.3

Rewrite the expression.

$4 x - 3 = 3 x + \frac{1}{3} \cdot 18 - 5$

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

Factor $3$ out of $18$ .

$4 x - 3 = 3 x + \frac{1}{3} \cdot (3 (6)) - 5$

Step 2.1.3.2

Cancel the common factor.

$4 x - 3 = 3 x + \frac{1}{3} \cdot (3 \cdot 6) - 5$

Step 2.1.3.3

Rewrite the expression.

$4 x - 3 = 3 x + 6 - 5$

Step 2.2

Subtract $5$ from $6$ .

$4 x - 3 = 3 x + 1$

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.

$4 x - 3 - 3 x = 1$

Step 3.2

Subtract $3 x$ from $4 x$ .

$x - 3 = 1$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$x = 1 + 3$

Step 4.2

Add $1$ and $3$ .

$x = 4$