To find the minimum and maximum values of x that satisfy the inequality ∣2x+6∣≤8, we need to consider two cases: when 2x+6 is non-negative (greater than or equal to 0) and when it is negative (less than 0).
Case 1: 2x+6 ≥ 0
In this case, we have ∣2x+6∣ = 2x+6.
So the inequality becomes 2x+6 ≤ 8.
Subtract 6 from both sides: 2x ≤ 2.
Divide both sides by 2: x ≤ 1.
Case 2: 2x+6 < 0
In this case, we have ∣2x+6∣ = -(2x+6) = -2x-6.
So the inequality becomes -2x-6 ≤ 8.
Add 6 to both sides: -2x ≤ 14.
Divide both sides by -2 and reverse the inequality sign: x ≥ -7.
Overall, the minimum value of x is -7 and the maximum value of x is 1.
Minimum: -7
Maximum: 1
What are the minimum and maximum values of x for which
∣2x+6∣≤8
Minimum:
Maximum:
1 answer