Question

Solve 3x - 7 > 5 or 2x + 6 < 12.
A. 3 < x < 4
B. -2/3 < x < 9
C. x > 4 or x < 3
D. no solution

Answer 1

The answer is C.

Answer 2

We have
\[3x-7>5\]
or
\[2x+6<12\]
Let's solve each of the inequality to find a condition for x
our answer will be the common part
\[3x-7>5\]
add 7 to both the sides
we'll get
\[3x>12\]
divide both sides by 3
\[x>4\]
now let's solve the second inequality
\[2x+6<12\]
subtract both sides by 6
\[2x<6\]
divide both sides by 2
\[x<3\]
So we see from one we get x<3 and from other x>4
this can't be simultaneously satisfied. There is no common condition
so
the answer is no solution

Answer 3

@ash2326
your work is fine, but I believe your conclusion is incorrect.
I believe it is C.
You stated x>4
x<3
The solution is in either region