Question

If $-2 < x \le 3,$ then find all possible values of $5x + 1.$ Give your answer in interval notation PLEASE ANSWER THUS PLEASE

Answer 1

Answer:

(-9,16]

Step-by-step explanation:

It is given that

$-2 < x \le 3$

We need to find the possible values of $5x+1$.

Multiply all sides by 5 in the above inequality.

$-2\cdot 5 < x\cdot 5 \le 3\cdot 5$

$-10< 5x\le 15$

Add 1 on each side.

$-10+1< 5x+1\le 15+1$

$-9< 5x+1\le 16$

It is clear that the possible values are lie between -9 and 16 (included).

$5x+1\in (-9,16]$

Close bracket represents that 16 is included in the solution set.

Therefore, the required interval is (-9,16].

Answer 2

Answer:

$(-9,16]$

Step-by-step explanation:

we know that

The domain of x is equal to the interval--------> $(-2,3]$

$-2< x \leq 3$

All real numbers greater than $-2$ and less than or equal to $3$

Let

$y=5x+1$

For $x=3$

$y=5x+1\\y=5(3)+1=16$

For $x>-2$

$y >5(-2)+1\\y > -9$

so

The range of the function is the interval--------> $(-9,16]$