The solution to this inequality is x<4
To graph the solution to the inequality, we'll need to follow these steps:
Solve the inequality for x.
Identify the shading region based on the inequality sign.
Draw the boundary line and shade the appropriate region.
Step 1: Solve the inequality for x:
Multiply both sides by 4:
3(x+8) > 2(2x+10)
Distribute both sides:
3x + 24 > 4x + 20
Move all x terms to one side:
-x + 24 > 20
Subtract 20 from both sides:
-x > -4
Multiply both sides by -1 (and flip the inequality sign):
x < 4
Step 2: Identify the shading region:
Since the inequality is <, we shade the region below the boundary line (the line representing x = 4).
Step 3: Draw the boundary line and shade the region:
Draw a dashed line at x = 4 (dashed because it's not part of the solution).
Shade the region below the dashed line.