Problem Solving

Which of the following expresses the range of possible values for t if 0 < |5t − 8| < 1?
A. 2/5 < t < 14/5
B. 2/5 < t < 9/5
C. 7/5 < t < 14/5
D. 7/5 < t < 9/5
E. 9/5 < t < 14/5
OA is D
How do i go about setting up the correct formular to solve this question? can any expert assist me?
Thank you

Roland2rule wrote:Which of the following expresses the range of possible values for t if 0 < |5t − 8| < 1?
A. 2/5 < t < 14/5
B. 2/5 < t < 9/5
C. 7/5 < t < 14/5
D. 7/5 < t < 9/5
E. 9/5 < t < 14/5
OA is D
How do i go about setting up the correct formular to solve this question? can any expert assist me?
Thank you

Since the absolute value of (5t - 8) is between 0 and 1 then the value of (5t - 8) must be between -1 and 1.

-1 < 5t - 8 < 1
7 < 5t < 9 (add 8 to both sides)
7/5 < t < 9/5 (divide both sides by 5)

Answer is D.

Hello, let's apply the definition of absolute value to 0 < |5t - 8| < 1. Hence, $$0<\left|5t-8\right|<1\ $$ $$-1<5t-8<1\ \ and\ \ \ \ 5t-8\ne0$$ $$7<5t<9\ \ and\ \ \ \ 5t\ne8$$ $$\frac{7}{5} < t < \frac{9}{5}\ \ and\ \ t\ne\ \frac{8}{5}.$$ Therefore, the correct option should be D.

We have to be carefull here because t cannot be 8/5.