Question

Solve 4x < 2x − 10 and -3x > -12. Which is the best description of the solution set?

Answer 1

First, solve 4x < 2x − 10
4x < 2x − 10
Subtract 2x from both sides.
4x - 2x < 2x -10 -2x
2x < -10
Divide both sides by coefficient of x, that is 2
2x/2 < -10/2
x < -5

Then, solve -3x > -12
Divide both sides by coefficient of x, that is -3. Since you're dividing both sides by a negative number, you need to change the direction of the sign too.
-3x > -12
-3x/-3 < -12/-3
x< 4

Now, draw that on a number line.


Since it's an 'and' case, we need to overlapping part.
Therefore, the solution is x<-5