Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Multiply $- 1$ by $6$ .

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

Step 2.1.3

Cancel the common factor of $6$ .

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Step 2.1.3.1

Move the leading negative in $- \frac{7}{6}$ into the numerator.

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

Step 2.1.3.2

Cancel the common factor.

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

Step 2.1.3.3

Rewrite the expression.

$- 1 - 6 x - 7 - 6 x \geq - 3 x$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $7$ from $- 1$ .

$- 6 x - 8 - 6 x \geq - 3 x$

Step 2.2.2

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

$- 12 x - 8 \geq - 3 x$

Step 3

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

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Step 3.1

Add $3 x$ to both sides of the inequality.

$- 12 x - 8 + 3 x \geq 0$

Step 3.2

Add $- 12 x$ and $3 x$ .

$- 9 x - 8 \geq 0$

Step 4

Add $8$ to both sides of the inequality.

$- 9 x \geq 8$

Step 5

Divide each term in $- 9 x \geq 8$ by $- 9$ and simplify.

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Step 5.1

Divide each term in $- 9 x \geq 8$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 x}{- 9} \leq \frac{8}{- 9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 9 x}{- 9} \leq \frac{8}{- 9}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{8}{- 9}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x \leq - \frac{8}{9}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{8}{9}$

Interval Notation:

$(- \infty, - \frac{8}{9}]$