Find all values of 
such that 
.
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+23254 Rewrite 8t² ≤ 3 - 10 t as 8t² + 10t - 3 ≤ 0
Factor: (4t - 1)(2t + 3) ≤ 0
Solve the related equality: (4t - 1)(2t + 3) = 0
If: 4t - 1 = 0 ---> 4t = 1 ---> t = 1/4
If: 2t + 3 = 0 ---> 2t = -3 ---> t = -3/2
These two points split the number line into three groups: t ≤ - 3/2 -3/2 ≤ t < 1/4 t ≥ 1/4
Pick any number for t such that t ≤ - 3/2; replace it into 8t² + 10t - 3
and check to see if that answer ≤ 0:
I'm going to try -10: 8(-10)² + 10(-10) - 3 = 697; since this number isn't ≤ 0, these numbers don't work.
Pick any number for t such that -3/2 ≤ t < 1/4
I'm going to try 0: 8(0)² + 10(0) - 3 = -3; since this aswer is less than zero, these numbers work.
Pick any number for t such that t ≥ 1/4:
I'm goint to try 1: 8(1)² + 10(1) - 3 = 15; since this answer isn't ≤ 0, these numbers don't work.
Answer: -3/2 ≤ t < 1/4
+23254 Rewrite 8t² ≤ 3 - 10 t as 8t² + 10t - 3 ≤ 0
Factor: (4t - 1)(2t + 3) ≤ 0
Solve the related equality: (4t - 1)(2t + 3) = 0
If: 4t - 1 = 0 ---> 4t = 1 ---> t = 1/4
If: 2t + 3 = 0 ---> 2t = -3 ---> t = -3/2
These two points split the number line into three groups: t ≤ - 3/2 -3/2 ≤ t < 1/4 t ≥ 1/4
Pick any number for t such that t ≤ - 3/2; replace it into 8t² + 10t - 3
and check to see if that answer ≤ 0:
I'm going to try -10: 8(-10)² + 10(-10) - 3 = 697; since this number isn't ≤ 0, these numbers don't work.
Pick any number for t such that -3/2 ≤ t < 1/4
I'm going to try 0: 8(0)² + 10(0) - 3 = -3; since this aswer is less than zero, these numbers work.
Pick any number for t such that t ≥ 1/4:
I'm goint to try 1: 8(1)² + 10(1) - 3 = 15; since this answer isn't ≤ 0, these numbers don't work.
Answer: -3/2 ≤ t < 1/4
