Define a variable and write an inequality for each problem. Then solve.

Question

Four times the sum of twice a number and –3 is less than 5.5 times that same number.

Answer 1

4(2x + -3) < 5.5x

8x + -12 < 5.5x

8x - 5.5x + -12 < 0

2.5x + -12 < 0

2.5x < 12

25x < 120

x < 120/25 = 24/5 = 4.8

final answer x < 4.8

Answer 2

When you work through these kinds of problems, it helps to try to write the equation out as you read it.

Here I'm replacing "a number" with x:

4*(2x + (-3)) < 5.5x

^Read the statement again while looking at how I wrote this to try to figure out how I translated the sentence into an equation.

Adding a negative number is the same as subtracting.

4(2x - 3) < 5.5x

Multiply the four by each term in the parentheses (distributive property).

8x - 12 < 5.5x

Subtract 5.5x on both sides of the inequality to combine the terms that have x.

2.5x - 12 < 0

Add 12 to both sides to get the term with x by itself.

2.5x < 12

Divide by 2.5 on both sides to get x by itself.

x < 4.8