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

Question

can you please assist and show graph number line 

Answer 1

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