sammy s.

asked • 09/09/16# Solve the inequality. Write the solution set using interval notation and graph the solution set on a number line: -6x+2=2(5-x).

can you please assist and show graph number line

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## 1 Expert Answer

Andrew M. answered • 09/09/16

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

As shown you have an equality, not an inequality.

-6x+2=2(5-x) distribute through parenthesis

-6x+2=2(5)+2(-x)

-6x+2=10-2x add 2x to both sides

2x-6x+2=10-2x+2x

-4x+2=10 subtract 2 from both sides

-4x+2-2=10-2

-4x=8 divide both sides by -4

-4x/(-4) = 8/(-4)

x = -2

With the ≥ or ≤ sign you would solve the exact same way

except for the point where when dividing both sides by

-4 requires you to reverse the inequality.

Your final answer is either

x≥-2 if your initial inequality was

6x+2≤2(5-x)

OR

x≤-2

if your initial inequality was

6x+2≥2(x-2)

Graphing on number line.

Let's take the answer x ≥ -2

since ther is an equality draw a closed dot at the point x=-2

indicating the point is included in the answer

Draw a ray withan arrow running the the right from that point

indicating all points to the right of -2 are included

----|----*→

-3 -2

Sorry, the drawing capacities here are very limited.

If it was x≤-2 the arrow would point left instead of right

sammy s.

-6x+2≥2(5-x) is what I meant

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09/09/16

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Andrew M.

09/09/16