Pre-Algebra Examples

$5 x + 2 < 3 (x - 3)$

Step 1

Simplify $3 (x - 3)$ .

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Step 1.1

Rewrite.

$5 x + 2 < 0 + 0 + 3 (x - 3)$

Step 1.2

Simplify by adding zeros.

$5 x + 2 < 3 (x - 3)$

Step 1.3

Apply the distributive property.

$5 x + 2 < 3 x + 3 \cdot - 3$

Step 1.4

Multiply $3$ by $- 3$ .

$5 x + 2 < 3 x - 9$

Step 2

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

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Step 2.1

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

$5 x + 2 - 3 x < - 9$

Step 2.2

Subtract $3 x$ from $5 x$ .

$2 x + 2 < - 9$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the inequality.

$2 x < - 9 - 2$

Step 3.2

Subtract $2$ from $- 9$ .

$2 x < - 11$

Step 4

Divide each term in $2 x < - 11$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 x < - 11$ by $2$ .

$\frac{2 x}{2} < \frac{- 11}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} < \frac{- 11}{2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 11}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x < - \frac{11}{2}$

Step 5