Find the range of possible values for x
3x-5 <37 and 2x+3>27
To find the range of possible values for x, we need to solve both inequalities separately and then combine the solutions.
Let's start with the first inequality:
3x - 5 < 37
To isolate x, we can add 5 to both sides of the inequality:
3x - 5 + 5 < 37 + 5
3x < 42
Next, divide both sides by 3:
3x/3 < 42/3
x < 14
Now let's move on to the second inequality:
2x + 3 > 27
To isolate x, we can subtract 3 from both sides:
2x + 3 - 3 > 27 - 3
2x > 24
Divide both sides by 2:
2x/2 > 24/2
x > 12
Now we have found the individual solutions for each inequality.
To find the range of possible values for x, we need to find the common values that satisfy both conditions.
From the first inequality, we have x < 14, and from the second inequality, we have x > 12.
Combining these conditions, we get:
12 < x < 14
So, the range of possible values for x is any real number between 12 and 14, excluding 12 and 14 themselves.