Question

Find the integer values of x that satisfy both of these inequalities.

5 − 3x ⩽ 7 and 4x + 1 < 13

Answer 1

x ∈ [-2/3, 3)

Explanation:

5 − 3x ⩽ 7 and 4x + 1 < 13, this is given

-3x ≤ 7-5 and 4x < 13 -1, subtract 5 from first inequality and subtract -1 from second

-3x ≤ 2 and 4x < 12, combine like terms

x ≥ -2/3 and x < 12/4, divide by -3 and change the first inequality, and divide the second inequality by 4

x ≥ -2/3 and x < 3

[-2/3, ∞) and (-∞, 3)

x ∈ [-2/3, 3)

Answer 2

0, 1, 2.

Explanation:

5 - 3x <= 7

-3x <= 2

x >= -2/3 (the inequality sign flips as we are dividing by a negative value)

4x + 1 < 13

4x < 12

x < 3.

So the integer values satisfying the inequalities are>

0, 1, 2.