Question

The sum of a number and 2 is no more than 6 or no less than 10

i need to define the variable , write a compound inequality and solve.

Answer 1

a. x + 2 ≤ 6 or x + 2 ≥ 10 b. x ≤ 4 or x ≥ 8

Explanation:

a. Write a compound inequality

Let x be the number.

Since x + 2 is no more than 6 then x + 2 ≤ 6 and x + 2 is no less than 10 then x + 2 ≥ 10

So, the compound inequality is x + 2 ≤ 6 or x + 2 ≥ 10

b. Solve the inequality

Solving each inequality, we have,

x + 2 ≤ 6

x ≤ 6 - 2

x ≤ 4

x + 2 ≥ 10

x ≥ 10 - 2

x ≥ 8

So, x ≤ 4 or x ≥ 8