Algebra Examples

$- 3 \leq - 6 x + 7 (x - \frac{3}{5}) - 1$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$- 6 x + 7 (x - \frac{3}{5}) - 1 \geq - 3$

Step 2

Simplify $- 6 x + 7 (x - \frac{3}{5}) - 1$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 6 x + 7 x + 7 (- \frac{3}{5}) - 1 \geq - 3$

Step 2.1.2

Multiply $7 (- \frac{3}{5})$ .

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Step 2.1.2.1

Multiply $- 1$ by $7$ .

$- 6 x + 7 x - 7 (\frac{3}{5}) - 1 \geq - 3$

Step 2.1.2.2

Combine $- 7$ and $\frac{3}{5}$ .

$- 6 x + 7 x + \frac{- 7 \cdot 3}{5} - 1 \geq - 3$

Step 2.1.2.3

Multiply $- 7$ by $3$ .

$- 6 x + 7 x + \frac{- 21}{5} - 1 \geq - 3$

Step 2.1.3

Move the negative in front of the fraction.

$- 6 x + 7 x - \frac{21}{5} - 1 \geq - 3$

Step 2.2

Add $- 6 x$ and $7 x$ .

$x - \frac{21}{5} - 1 \geq - 3$

Step 2.3

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x - \frac{21}{5} - 1 \cdot \frac{5}{5} \geq - 3$

Step 2.4

Combine $- 1$ and $\frac{5}{5}$ .

$x - \frac{21}{5} + \frac{- 1 \cdot 5}{5} \geq - 3$

Step 2.5

Combine the numerators over the common denominator.

$x + \frac{- 21 - 1 \cdot 5}{5} \geq - 3$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 1$ by $5$ .

$x + \frac{- 21 - 5}{5} \geq - 3$

Step 2.6.2

Subtract $5$ from $- 21$ .

$x + \frac{- 26}{5} \geq - 3$

Step 2.7

Move the negative in front of the fraction.

$x - \frac{26}{5} \geq - 3$

Step 3

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

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Step 3.1

Add $\frac{26}{5}$ to both sides of the inequality.

$x \geq - 3 + \frac{26}{5}$

Step 3.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x \geq - 3 \cdot \frac{5}{5} + \frac{26}{5}$

Step 3.3

Combine $- 3$ and $\frac{5}{5}$ .

$x \geq \frac{- 3 \cdot 5}{5} + \frac{26}{5}$

Step 3.4

Combine the numerators over the common denominator.

$x \geq \frac{- 3 \cdot 5 + 26}{5}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 3$ by $5$ .

$x \geq \frac{- 15 + 26}{5}$

Step 3.5.2

Add $- 15$ and $26$ .

$x \geq \frac{11}{5}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{11}{5}$

Interval Notation:

$[\frac{11}{5}, \infty)$