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# –x + 3 > 7

### 4 Answers by Expert Tutors

Lisa I. | Math tutor specializing in algebraMath tutor specializing in algebra
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-x + 3 > 7

-x + 3 - 3 > 7 - 3    This step is straightforward and the same as an equality.

-x > 4    It's this next step that confuses a lot of students.

-x/-1 < 4/-1   When you divide out the negative, you flip the sign

So the solution is x < -4

To understand why, it helps if you draw a number line and think about what it means. If negative x is greater than 4, x itself must be a negative number and has to be less than -4.

(x)...(-4)...(-3)...(-2)...(-1)...(0)...(1)...(2)...(3)...(4)...(-x)

Jon G. | Patient knowledgeable STEM educator/former healthcare practitionerPatient knowledgeable STEM educator/form...
4.9 4.9 (7 lesson ratings) (7)
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Trevor R. | Math/physics: Georgia Tech grad, at KSU for Master's in TeachingMath/physics: Georgia Tech grad, at KSU ...
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Subtract 3 from both sides:

-x +3 - 3 > 7 - 3
-x > 4

Multiply each side by -1:

(-x)*(-1) > (4)*(-1)

When you multiply or divide by a negative number, you also have to flip the inequality symbol.