Answer:
-1<x<7
Step-by-step explanation:
We need to solve each inequality and then from the interval of numbers they both have in common (doing this because of the 'and').
x-2<5
Add 2 on both sides:
x<5+2
Simplify:
x<7
These are values of x that are less than 7.
x+7>6
Subtract 7 on both sides:
x>6-7
Simplify:
x>-1
These are values of x greater than -1.
So the values they have in common are the numbers in between -1 and 7.
That is x<7 and x>-1.
You can also write it as -1<x<7.
Maybe you need a graph to convince you more.
○~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~○
‐-------------(-1)------------------------(7)-----------------
So where you see both graphs is the solution:
○~~~~~~~~~~~~~~○
‐-------------(-1)------------------------(7)-----------------