Pre-Algebra Examples

$3 (x - 4) - 5 (2 - x) < 16 - 2 (3 x - 2)$

Step 1

Simplify $3 (x - 4) - 5 (2 - x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 x + 3 \cdot - 4 - 5 (2 - x) < 16 - 2 (3 x - 2)$

Step 1.1.2

Multiply $3$ by $- 4$ .

$3 x - 12 - 5 (2 - x) < 16 - 2 (3 x - 2)$

Step 1.1.3

Apply the distributive property.

$3 x - 12 - 5 \cdot 2 - 5 (- x) < 16 - 2 (3 x - 2)$

Step 1.1.4

Multiply $- 5$ by $2$ .

$3 x - 12 - 10 - 5 (- x) < 16 - 2 (3 x - 2)$

Step 1.1.5

Multiply $- 1$ by $- 5$ .

$3 x - 12 - 10 + 5 x < 16 - 2 (3 x - 2)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $3 x$ and $5 x$ .

$8 x - 12 - 10 < 16 - 2 (3 x - 2)$

Step 1.2.2

Subtract $10$ from $- 12$ .

$8 x - 22 < 16 - 2 (3 x - 2)$

Step 2

Simplify $16 - 2 (3 x - 2)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$8 x - 22 < 16 - 2 (3 x) - 2 \cdot - 2$

Step 2.1.2

Multiply $3$ by $- 2$ .

$8 x - 22 < 16 - 6 x - 2 \cdot - 2$

Step 2.1.3

Multiply $- 2$ by $- 2$ .

$8 x - 22 < 16 - 6 x + 4$

Step 2.2

Add $16$ and $4$ .

$8 x - 22 < - 6 x + 20$

Step 3

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

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Step 3.1

Add $6 x$ to both sides of the inequality.

$8 x - 22 + 6 x < 20$

Step 3.2

Add $8 x$ and $6 x$ .

$14 x - 22 < 20$

Step 4

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

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Step 4.1

Add $22$ to both sides of the inequality.

$14 x < 20 + 22$

Step 4.2

Add $20$ and $22$ .

$14 x < 42$

Step 5

Divide each term in $14 x < 42$ by $14$ and simplify.

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Step 5.1

Divide each term in $14 x < 42$ by $14$ .

$\frac{14 x}{14} < \frac{42}{14}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $14$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{14 x}{14} < \frac{42}{14}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x < \frac{42}{14}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $42$ by $14$ .

$x < 3$

Step 6