Solve the Inequality for k -1/3(k+3)<=6

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

Step 1

Multiply each term in $- \frac{1}{3} \cdot (k + 3) \leq 6$ by $- 3$ to eliminate the fractions.

Multiply each term in $- \frac{1}{3} \cdot (k + 3) \leq 6$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{1}{3} \cdot (k + 3) \cdot - 3 \geq 6 \cdot - 3$

Simplify the left side.

Apply the distributive property.

$(- \frac{1}{3} k - \frac{1}{3} \cdot 3) \cdot - 3 \geq 6 \cdot - 3$

Combine $k$ and $\frac{1}{3}$ .

$(- \frac{k}{3} - \frac{1}{3} \cdot 3) \cdot - 3 \geq 6 \cdot - 3$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$(- \frac{k}{3} + \frac{- 1}{3} \cdot 3) \cdot - 3 \geq 6 \cdot - 3$

Cancel the common factor.

$(- \frac{k}{3} + \frac{- 1}{3} \cdot 3) \cdot - 3 \geq 6 \cdot - 3$

Rewrite the expression.

$(- \frac{k}{3} - 1) \cdot - 3 \geq 6 \cdot - 3$

Apply the distributive property.

$- \frac{k}{3} \cdot - 3 - 1 \cdot - 3 \geq 6 \cdot - 3$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{k}{3}$ into the numerator.

$\frac{- k}{3} \cdot - 3 - 1 \cdot - 3 \geq 6 \cdot - 3$

Factor $3$ out of $- 3$ .

$\frac{- k}{3} \cdot (3 (- 1)) - 1 \cdot - 3 \geq 6 \cdot - 3$

Cancel the common factor.

$\frac{- k}{3} \cdot (3 \cdot - 1) - 1 \cdot - 3 \geq 6 \cdot - 3$

Rewrite the expression.

$- k \cdot - 1 - 1 \cdot - 3 \geq 6 \cdot - 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 k - 1 \cdot - 3 \geq 6 \cdot - 3$

Multiply $k$ by $1$ .

$k - 1 \cdot - 3 \geq 6 \cdot - 3$

Multiply $- 1$ by $- 3$ .

$k + 3 \geq 6 \cdot - 3$

Simplify the right side.

Multiply $6$ by $- 3$ .

$k + 3 \geq - 18$

Step 2

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

Subtract $3$ from both sides of the inequality.

$k \geq - 18 - 3$

Subtract $3$ from $- 18$ .

$k \geq - 21$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$k \geq - 21$

Interval Notation:

$[- 21, \infty)$

Solve the Inequality for k -1/3(k+3)<=6

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