Answer this question step by step please. Thank you!

## –x + 3 > 7

# 4 Answers

-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)

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.

Final answer:

x < -4

-x +3 > 7

The greater than or less than signs act the same as an equal sign. First we want to isolate the letter. To do that we need to move the +3 over to the other side of the equation. Since the problem says +3 we are going to do the opposite of -3 to both sides of the equation. +3-3= 0 so the three on the left side of the inequality sign cancels out. 7-3 = 4. Now the equation should read -x > 4. You want the letter to be positive so we need to multiply the whole equation by -1. -x times -1 gives you a positive x. Positive 4 times -1 gives you negative 4 so the answer is x = -4