Question

Select the solution set of $-1<2x+3\le 10$ from given options

• A. {1,2,3}
• B. {1,2,3,4}
• C. {2,3,4}
• D. {2,3,4,5}

Answer 1

The correct option is A {1,2,3}

$-1<2x+3\le 10$
Subtract 3 from each sides
$-1-3<2x+3-3\le 10-3$
$-4<2x\le 7$
Divide by 2 each side
$-\frac{4}{2}<\frac{2x}{2}\le \frac{7}{2}$
$-2<x\le 3.5$
From here we can say that x will that all the value between -2 to 3.5 [including 3.5 because $\le$ sign].

Now lets look at options

A) {1,2,3}
B) {1,2,3,4} $\to$ not possible because 4 is not in the range
C) {2,3,4} $\to$ same reason
D) {2,3,4,5} $\to$ Same reason