Algebra Examples

$2 (x - 4) \leq 2 + 3 (x - 6)$

Step 1

Solve $x \geq 8$ .

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Step 1.1

Simplify $2 (x - 4)$ .

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Step 1.1.1

Rewrite.

$0 + 0 + 2 (x - 4) \leq 2 + 3 (x - 6)$

Step 1.1.2

Simplify by adding zeros.

$2 (x - 4) \leq 2 + 3 (x - 6)$

Step 1.1.3

Apply the distributive property.

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

Step 1.1.4

Multiply $2$ by $- 4$ .

$2 x - 8 \leq 2 + 3 (x - 6)$

Step 1.2

Simplify $2 + 3 (x - 6)$ .

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Apply the distributive property.

$2 x - 8 \leq 2 + 3 x + 3 \cdot - 6$

Step 1.2.1.2

Multiply $3$ by $- 6$ .

$2 x - 8 \leq 2 + 3 x - 18$

Step 1.2.2

Subtract $18$ from $2$ .

$2 x - 8 \leq 3 x - 16$

Step 1.3

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

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Step 1.3.1

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

$2 x - 8 - 3 x \leq - 16$

Step 1.3.2

Subtract $3 x$ from $2 x$ .

$- x - 8 \leq - 16$

Step 1.4

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

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Step 1.4.1

Add $8$ to both sides of the inequality.

$- x \leq - 16 + 8$

Step 1.4.2

Add $- 16$ and $8$ .

$- x \leq - 8$

Step 1.5

Divide each term in $- x \leq - 8$ by $- 1$ and simplify.

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Step 1.5.1

Divide each term in $- x \leq - 8$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{- 8}{- 1}$

Step 1.5.2

Simplify the left side.

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Step 1.5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{- 8}{- 1}$

Step 1.5.2.2

Divide $x$ by $1$ .

$x \geq \frac{- 8}{- 1}$

Step 1.5.3

Simplify the right side.

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Step 1.5.3.1

Divide $- 8$ by $- 1$ .

$x \geq 8$

Step 2

Use the inequality $x \geq 8$ to build the set notation.

${x | x \geq 8}$

Step 3