College Algebra

Question

Solve the following inequality and write the answer in interval notation.

-5<3x+2<3

Answer 1

-5 < 3*x + 2 < 3

Subtract 2 from both sides:

-5 - 2 < 3*x < 3 - 2

-7 < 3*x < 1

Divide the inequality throughout by 3:

-7/3 < x < 1/3

which is x ∈ (-7/3, 1/3) using a different notation.

Check:

i. Pick a whole number on the interval (-7/3, 1/3).

Let x = -2,

3(-2) + 2 = -6 + 2 = -4; satisfies the inequality: -5 < -4 < 3

ii. Pick another integer on the same interval (-7/3, 1/3).

Let x = 0,

3(0) + 2 = 0 + 2 = 2; satisfies the inequality: -5 < 0 < 3