Solve for x and graph the solution on the number line below.
−28≤3x−10and
23>3x−10
To solve the first inequality, we first add 10 to both sides to isolate the variable:
-28 + 10 ≤ 3x - 10 + 10
-18 ≤ 3x
Next, we divide both sides by 3, remembering to flip the inequality sign since we are dividing by a negative number:
-18/3 ≥ 3x/3
-6 ≥ x
So the solution to the first inequality is x ≤ -6.
To solve the second inequality, we add 10 to both sides to isolate the variable:
23 + 10 > 3x - 10 + 10
33 > 3x
Next, we divide both sides by 3:
33/3 > 3x/3
11 > x
So the solution to the second inequality is x < 11.
To graph the solution on the number line, we first draw a line with an arrow pointing to the left for the values less than or equal to -6. Next, we draw an open circle on 11 and draw an arrow pointing to the right for the values greater than 11.
Number line:
<---○=========================>
-6 11
The solution is all the values to the left of -6 and all the values greater than 11.