Answer:
Solution set in Interval notation: [-9,16]
Step-by-step explanation:
[tex]\text{If }-2\leq x\leq 3\text{ then find all possible value of 5x+1 in interval notation}[/tex]
Let y=5x+1 , we need to find solution of y in interval form.
[tex]-2\leq x\leq 3[/tex]
Multiply by 5 all sides of inequality
[tex]-2\times 5\leq 5x\leq 3\times 5[/tex]
[tex]-10\leq 5x\leq 15[/tex]
Add 1 all three sides of inequality
[tex]-10+1\leq 5x+1\leq 15+1[/tex]
[tex]-9\leq 5x+1\leq 16[/tex]
[tex]\therefore -9\leq y\leq 16[/tex]
Thus, Solution set in Interval notation: [-9,16]
