Algebra Examples

$- \frac{d}{12} - 6 < 1$

Step 1

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

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Step 1.1

Add $6$ to both sides of the inequality.

$- \frac{d}{12} < 1 + 6$

Step 1.2

Add $1$ and $6$ .

$- \frac{d}{12} < 7$

Step 2

Divide each term in $- \frac{d}{12} < 7$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- \frac{d}{12} < 7$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{d}{12}}{- 1} > \frac{7}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{d}{12}}{1} > \frac{7}{- 1}$

Step 2.2.2

Divide $\frac{d}{12}$ by $1$ .

$\frac{d}{12} > \frac{7}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $7$ by $- 1$ .

$\frac{d}{12} > - 7$

Step 3

Multiply both sides by $12$ .

$\frac{d}{12} \cdot 12 > - 7 \cdot 12$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $12$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{d}{12} \cdot 12 > - 7 \cdot 12$

Step 4.1.1.2

Rewrite the expression.

$d > - 7 \cdot 12$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 7$ by $12$ .

$d > - 84$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$d > - 84$

Interval Notation:

$(- 84, \infty)$