Pre-Algebra Examples

$4 (8 - 2 x) + 2 x < 5 (9 + 3 x)$

Step 1

Simplify $4 (8 - 2 x) + 2 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 \cdot 8 + 4 (- 2 x) + 2 x < 5 (9 + 3 x)$

Step 1.1.2

Multiply $4$ by $8$ .

$32 + 4 (- 2 x) + 2 x < 5 (9 + 3 x)$

Step 1.1.3

Multiply $- 2$ by $4$ .

$32 - 8 x + 2 x < 5 (9 + 3 x)$

Step 1.2

Add $- 8 x$ and $2 x$ .

$32 - 6 x < 5 (9 + 3 x)$

Step 2

Simplify $5 (9 + 3 x)$ .

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Step 2.1

Apply the distributive property.

$32 - 6 x < 5 \cdot 9 + 5 (3 x)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $5$ by $9$ .

$32 - 6 x < 45 + 5 (3 x)$

Step 2.2.2

Multiply $3$ by $5$ .

$32 - 6 x < 45 + 15 x$

Step 3

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

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Step 3.1

Subtract $15 x$ from both sides of the inequality.

$32 - 6 x - 15 x < 45$

Step 3.2

Subtract $15 x$ from $- 6 x$ .

$32 - 21 x < 45$

Step 4

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

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Step 4.1

Subtract $32$ from both sides of the inequality.

$- 21 x < 45 - 32$

Step 4.2

Subtract $32$ from $45$ .

$- 21 x < 13$

Step 5

Divide each term in $- 21 x < 13$ by $- 21$ and simplify.

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Step 5.1

Divide each term in $- 21 x < 13$ by $- 21$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 21 x}{- 21} > \frac{13}{- 21}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 21$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 21 x}{- 21} > \frac{13}{- 21}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{13}{- 21}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x > - \frac{13}{21}$

Step 6