Algebra Examples

$3 - 5 (2 x + 1) \leq 10$

Step 1

Solve $x \geq - \frac{6}{5}$ .

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Step 1.1

Simplify $3 - 5 (2 x + 1)$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$3 - 5 (2 x) - 5 \cdot 1 \leq 10$

Step 1.1.1.2

Multiply $2$ by $- 5$ .

$3 - 10 x - 5 \cdot 1 \leq 10$

Step 1.1.1.3

Multiply $- 5$ by $1$ .

$3 - 10 x - 5 \leq 10$

Step 1.1.2

Subtract $5$ from $3$ .

$- 10 x - 2 \leq 10$

Step 1.2

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

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Step 1.2.1

Add $2$ to both sides of the inequality.

$- 10 x \leq 10 + 2$

Step 1.2.2

Add $10$ and $2$ .

$- 10 x \leq 12$

Step 1.3

Divide each term in $- 10 x \leq 12$ by $- 10$ and simplify.

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Step 1.3.1

Divide each term in $- 10 x \leq 12$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 x}{- 10} \geq \frac{12}{- 10}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 10$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 10 x}{- 10} \geq \frac{12}{- 10}$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{12}{- 10}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Cancel the common factor of $12$ and $- 10$ .

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Step 1.3.3.1.1

Factor $2$ out of $12$ .

$x \geq \frac{2 (6)}{- 10}$

Step 1.3.3.1.2

Cancel the common factors.

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Step 1.3.3.1.2.1

Factor $2$ out of $- 10$ .

$x \geq \frac{2 \cdot 6}{2 \cdot - 5}$

Step 1.3.3.1.2.2

Cancel the common factor.

$x \geq \frac{2 \cdot 6}{2 \cdot - 5}$

Step 1.3.3.1.2.3

Rewrite the expression.

$x \geq \frac{6}{- 5}$

Step 1.3.3.2

Move the negative in front of the fraction.

$x \geq - \frac{6}{5}$

Step 2

Use the inequality $x \geq - \frac{6}{5}$ to build the set notation.

${x | x \geq - \frac{6}{5}}$

Step 3