Solve the Inequality for k -10-(-8k-7)>3k-10-4k

$- 10 - (- 8 k - 7) > 3 k - 10 - 4 k$

Step 1

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

$3 k - 10 - 4 k < - 10 - (- 8 k - 7)$

Step 2

Subtract $4 k$ from $3 k$ .

$- k - 10 < - 10 - (- 8 k - 7)$

Step 3

Simplify $- 10 - (- 8 k - 7)$ .

Simplify each term.

Apply the distributive property.

$- k - 10 < - 10 - (- 8 k) - - 7$

Multiply $- 8$ by $- 1$ .

$- k - 10 < - 10 + 8 k - - 7$

Multiply $- 1$ by $- 7$ .

$- k - 10 < - 10 + 8 k + 7$

Add $- 10$ and $7$ .

$- k - 10 < 8 k - 3$

Step 4

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

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

$- k - 10 - 8 k < - 3$

Subtract $8 k$ from $- k$ .

$- 9 k - 10 < - 3$

Step 5

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

Add $10$ to both sides of the inequality.

$- 9 k < - 3 + 10$

Add $- 3$ and $10$ .

$- 9 k < 7$

Step 6

Divide each term in $- 9 k < 7$ by $- 9$ and simplify.

Divide each term in $- 9 k < 7$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 k}{- 9} > \frac{7}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 k}{- 9} > \frac{7}{- 9}$

Divide $k$ by $1$ .

$k > \frac{7}{- 9}$

Simplify the right side.

Move the negative in front of the fraction.

$k > - \frac{7}{9}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$k > - \frac{7}{9}$

Interval Notation:

$(- \frac{7}{9}, \infty)$

Solve the Inequality for k -10-(-8k-7)>3k-10-4k

Related Questions

Support LCMGCF.com by disabling your adblocker.