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How do you solve #-\frac { 3} { 5} k + 4\leq - \frac { 1} { 5} k#?

Answer 1

Eva Abramson

#k>=10#

Refer to the explanation for the process.

Solve:

#-3/5k+4<=-1/5k#

Simplify.

#-(3k)/5+4<=-k/5#

Multiply both sides by #5#.

#5xx-(3k)/5+4xx5<=-k/5xx5#

Cancel #5# on both sides . #color(red)cancel(color(black)(5))^1xx-(3k)/color(red)cancel(color(black)(5))^1+4xx5<=-k/color(red)cancel(color(black)(5))^1xxcolor(red)cancel(color(black)(5))^1#

Simplify.

#-3k+20<=-k#

Add #3k# to both sides.

#20<=-k+3k#

Simplify.

#20<=2k#

Divide both sides by #2#.

#20/2<=k#

Simplify.

#10<=k#

Switch sides.

#k>=10#

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Answer 2

Jace Anderson

To solve the inequality (-\frac{3}{5}k + 4 \leq -\frac{1}{5}k), follow these steps:

Subtract (-\frac{3}{5}k) from both sides of the inequality: [4 \leq -\frac{1}{5}k + \frac{3}{5}k]
Simplify the expression on the right side of the inequality: [4 \leq \frac{2}{5}k]
Multiply both sides of the inequality by (\frac{5}{2}) to isolate (k): [4 \times \frac{5}{2} \leq \frac{2}{5}k \times \frac{5}{2}] [10 \leq k]

So, the solution to the inequality is (k \geq 10).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.