Solve the Inequality for d -10+2(-9d+8)<6d+10-2

$- 10 + 2 (- 9 d + 8) < 6 d + 10 - 2$

Step 1

Simplify $- 10 + 2 (- 9 d + 8)$ .

Simplify each term.

Apply the distributive property.

$- 10 + 2 (- 9 d) + 2 \cdot 8 < 6 d + 10 - 2$

Multiply $- 9$ by $2$ .

$- 10 - 18 d + 2 \cdot 8 < 6 d + 10 - 2$

Multiply $2$ by $8$ .

$- 10 - 18 d + 16 < 6 d + 10 - 2$

Add $- 10$ and $16$ .

$- 18 d + 6 < 6 d + 10 - 2$

Step 2

Subtract $2$ from $10$ .

$- 18 d + 6 < 6 d + 8$

Step 3

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

Subtract $6 d$ from both sides of the inequality.

$- 18 d + 6 - 6 d < 8$

Subtract $6 d$ from $- 18 d$ .

$- 24 d + 6 < 8$

Step 4

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

Subtract $6$ from both sides of the inequality.

$- 24 d < 8 - 6$

Subtract $6$ from $8$ .

$- 24 d < 2$

Step 5

Divide each term in $- 24 d < 2$ by $- 24$ and simplify.

Divide each term in $- 24 d < 2$ by $- 24$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 24 d}{- 24} > \frac{2}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 d}{- 24} > \frac{2}{- 24}$

Divide $d$ by $1$ .

$d > \frac{2}{- 24}$

Simplify the right side.

Cancel the common factor of $2$ and $- 24$ .

Factor $2$ out of $2$ .

$d > \frac{2 (1)}{- 24}$

Cancel the common factors.

Factor $2$ out of $- 24$ .

$d > \frac{2 \cdot 1}{2 \cdot - 12}$

Cancel the common factor.

$d > \frac{2 \cdot 1}{2 \cdot - 12}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \frac{1}{12}, \infty)$

Solve the Inequality for d -10+2(-9d+8)<6d+10-2

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