Pre-Algebra Examples

$\frac{2 x + 4}{3} < 6 x - 7$

Step 1

Multiply both sides by $3$ .

$\frac{2 x + 4}{3} \cdot 3 < (6 x - 7) \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2 x + 4}{3} \cdot 3$ .

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Step 2.1.1.1

Factor $2$ out of $2 x + 4$ .

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Step 2.1.1.1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 4}{3} \cdot 3 < (6 x - 7) \cdot 3$

Step 2.1.1.1.2

Factor $2$ out of $4$ .

$\frac{2 x + 2 \cdot 2}{3} \cdot 3 < (6 x - 7) \cdot 3$

Step 2.1.1.1.3

Factor $2$ out of $2 x + 2 \cdot 2$ .

$\frac{2 (x + 2)}{3} \cdot 3 < (6 x - 7) \cdot 3$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{2 (x + 2)}{3} \cdot 3 < (6 x - 7) \cdot 3$

Step 2.1.1.2.2

Rewrite the expression.

$2 (x + 2) < (6 x - 7) \cdot 3$

Step 2.1.1.3

Apply the distributive property.

$2 x + 2 \cdot 2 < (6 x - 7) \cdot 3$

Step 2.1.1.4

Multiply $2$ by $2$ .

$2 x + 4 < (6 x - 7) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(6 x - 7) \cdot 3$ .

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Step 2.2.1.1

Apply the distributive property.

$2 x + 4 < 6 x \cdot 3 - 7 \cdot 3$

Step 2.2.1.2

Multiply.

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Step 2.2.1.2.1

Multiply $3$ by $6$ .

$2 x + 4 < 18 x - 7 \cdot 3$

Step 2.2.1.2.2

Multiply $- 7$ by $3$ .

$2 x + 4 < 18 x - 21$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $18 x$ from both sides of the inequality.

$2 x + 4 - 18 x < - 21$

Step 3.1.2

Subtract $18 x$ from $2 x$ .

$- 16 x + 4 < - 21$

Step 3.2

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

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Step 3.2.1

Subtract $4$ from both sides of the inequality.

$- 16 x < - 21 - 4$

Step 3.2.2

Subtract $4$ from $- 21$ .

$- 16 x < - 25$

Step 3.3

Divide each term in $- 16 x < - 25$ by $- 16$ and simplify.

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Step 3.3.1

Divide each term in $- 16 x < - 25$ by $- 16$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 16 x}{- 16} > \frac{- 25}{- 16}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 16$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 16 x}{- 16} > \frac{- 25}{- 16}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 25}{- 16}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Dividing two negative values results in a positive value.

$x > \frac{25}{16}$

Step 4