Solve the Inequality for k 10-2(8k+6)>8k+3+2

$10 - 2 (8 k + 6) > 8 k + 3 + 2$

Step 1

Simplify $10 - 2 (8 k + 6)$ .

Simplify each term.

Apply the distributive property.

$10 - 2 (8 k) - 2 \cdot 6 > 8 k + 3 + 2$

Multiply $8$ by $- 2$ .

$10 - 16 k - 2 \cdot 6 > 8 k + 3 + 2$

Multiply $- 2$ by $6$ .

$10 - 16 k - 12 > 8 k + 3 + 2$

Subtract $12$ from $10$ .

$- 16 k - 2 > 8 k + 3 + 2$

Step 2

Add $3$ and $2$ .

$- 16 k - 2 > 8 k + 5$

Step 3

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

Subtract $8 k$ from both sides of the inequality.

$- 16 k - 2 - 8 k > 5$

Subtract $8 k$ from $- 16 k$ .

$- 24 k - 2 > 5$

Step 4

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

Add $2$ to both sides of the inequality.

$- 24 k > 5 + 2$

Add $5$ and $2$ .

$- 24 k > 7$

Step 5

Divide each term in $- 24 k > 7$ by $- 24$ and simplify.

Divide each term in $- 24 k > 7$ by $- 24$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 24 k}{- 24} < \frac{7}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 k}{- 24} < \frac{7}{- 24}$

Divide $k$ by $1$ .

$k < \frac{7}{- 24}$

Simplify the right side.

Move the negative in front of the fraction.

$k < - \frac{7}{24}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$k < - \frac{7}{24}$

Interval Notation:

$(- \infty, - \frac{7}{24})$

Solve the Inequality for k 10-2(8k+6)>8k+3+2

Related Questions

Support LCMGCF.com by disabling your adblocker.