Algebra Examples

$5 (3 - 2 x) \geq 10$

Step 1

Divide each term in $5 (3 - 2 x) \geq 10$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 (3 - 2 x) \geq 10$ by $5$ .

$\frac{5 (3 - 2 x)}{5} \geq \frac{10}{5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 (3 - 2 x)}{5} \geq \frac{10}{5}$

Step 1.2.1.2

Divide $3 - 2 x$ by $1$ .

$3 - 2 x \geq \frac{10}{5}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $10$ by $5$ .

$3 - 2 x \geq 2$

Step 2

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

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Step 2.1

Subtract $3$ from both sides of the inequality.

$- 2 x \geq 2 - 3$

Step 2.2

Subtract $3$ from $2$ .

$- 2 x \geq - 1$

Step 3

Divide each term in $- 2 x \geq - 1$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 x \geq - 1$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{- 1}{- 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{- 1}{- 2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 1}{- 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$x \leq \frac{1}{2}$

Step 4

Convert the inequality to interval notation.

$(- \infty, \frac{1}{2}]$

Step 5