Linear inequalities

Question

Linear inequalities: three times a number decreased by seven is between -43 and 59

find the interval for valid values

Answer 1

Being between -43 and 59 means the value is greater than -43 and less than 59.

If "x" is "a number" then three times "x" is "3x" and decreasing this by seven means "3x - 7".

So there are two cases:

Case 1

3x - 7 > -43

3x > -36

x > -12

Case 2

3x - 7 < 59

3x < 66

x < 22

Therefore, the number must be greater than -12 but less than 22 which can be written in interval notation as (-12, 22) or as the inequality -12 < x < 22