Question

solve the inequality. state the solution set as an interval and graph the solution set.
$3(x - 40) - 4 > -x - 40$
the solution set as an interval is:
the graph of the solution set is:
16 17 18 19 20 21 22 23 24 25 26
clear all draw:

Explanation:

Step1: Expand left-hand side

$3(x-40)-4 = 3x - 120 - 4 = 3x - 124$

Step2: Rewrite the inequality

$3x - 124 > -x - 40$

Step3: Isolate $x$ terms on left

Add $x$ to both sides: $3x + x - 124 > -40$
$4x - 124 > -40$

Step4: Isolate constant terms on right

Add 124 to both sides: $4x > -40 + 124$
$4x > 84$

Step5: Solve for $x$

Divide by 4: $x > \frac{84}{4}$
$x > 21$

Answer:

The solution set as an interval is: $(21, \infty)$

For the graph:

1. Place an open circle at 21 on the number line.
2. Draw a ray pointing to the right from the open circle to represent all values greater than 21.