To solve the inequality, 12 - x > 5 < 2x - 2, we can break it down into two separate inequalities:
First inequality: 12 - x > 5
To isolate x, we subtract 12 from both sides:
12 - x - 12 > 5 - 12
-x > -7
Dividing both sides by -1, we flip the inequality sign:
x < 7
Second inequality: 5 < 2x - 2
To isolate x, we add 2 to both sides:
5 + 2 < 2x - 2 + 2
7 < 2x
Dividing both sides by 2, we get:
3.5 < x or x > 3.5
Combining the two inequalities, we have x < 7 and x > 3.5. We can represent this solution on a number line by shading the regions to the left of 7 and to the right of 3.5, indicating that any value of x in these regions satisfies the inequality.
Solve the inequality and represent the solution on a number line.
12- x >5< 2 x -2
1 answer