Question

what is the solution to this inequality
-5(x+3/10)greater than or equal to -7/2

Answer 1

Solve: -5(x + 3/10) ≥ -7/2

Method 1 (divide by -5, flip inequality):
x + 3/10 ≤ (-7/2)/(-5) = 7/10
x ≤ 7/10 - 3/10 = 4/10 = 2/5

Method 2 (expand):
-5x - 3/2 ≥ -7/2
-5x ≥ -7/2 + 3/2 = -2
x ≤ 2/5

Solution: x ≤ 2/5 (interval notation: (-∞, 2/5]).