Question

Write “five less than the product of three times a number and four is no more than sixty-seven” as an algebraic expression. Solve and graph it.

Answer 1

The inequality would be 3x(4)-5≤67; the solution is x≤6; the graph is attached.

To solve this, first multiply the coefficients of x:
12x-5≤67

Add 5 to both sides:
12x-5+5≤67+5
12x≤72

Divide both sides by 12:
12x/12 ≤ 72/12
x ≤ 6

Answer 2

The inequality represented by this statement is:
3(x +4) - 5 < 67
3x + 12 - 5 < 67
3x + 7 < 67
3x   < 60
x < 20

To graph this you will draw a number line with 18, 19, 20, 21, and 22.  Directly above the 20, you will draw a filled in circle.  Draw and arrow pointing to the left off this circle.  This tells us that any numbers that are 20 or less would be part of the solution set.