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–x + 3 > 7

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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)

I'd like to add just a small bit of information to the previous 2 answers...which you can avoid if the previoius answers were much more helpful To begin with the equation... -4 + 3 > 7 -x + 3 > 7 Step 1: original equation* (in math, normally if there is a (-x) its easier to work when (x) is positive. Consider -x = (-1)(x) Correct? Well it is. So, let's get a positive 'x', okay (-1)(x) + 3 > 7 Step 2: Rewrite (-1)...which means the same thing (-1)(-1)(x) + 3 > 7(-1) Step 3: Balance equation...what you do to one of an equation, you gotta do to the other (1)(x) + 3 > -7 Step 4: the products of Step 3 x + 3 < -7 Step 5: Since we multiplied by (-1), the inequality sign needs to be inverted to (<)... Math Rule 302.91...(just kidding)...but the rule is 'when an inequality is multipied by a positive number, the sign remains the same...but when an inequality is multiplied by a negative number, the sign is reversed x + 3 < -7 Rewrite equation from above - 3 -3 Step 6: Subtract 3 on both sides, balance equation x + 0 < -7 - (-3) rewrite equaiton x + 0 < -7 + 3 Step 7: Change sign: subtracting a negative x < -4 Step 8: complete addition/subtraction operations Though I've outline more steps than 2 novels...this is really what one does when working with inequalities...and what the previous e-mails described, I'm just explain WHY we get the answer. The more you do these kinds of problems, the easier they will become and you'll be able to solve inequalities with 3 to 4 Steps...possibly even 2. Wow then that would be great and you'll be Master of Inequalities!! Yea!!;) Lastly(I know this is a lot...however, I hope this explain WHY we can solve inequalities and then proving/showing that the answer is going to work for the equation),when solving inequalities, the answer is usually then plotted on a number line... with the answer :) x < -4 Number line:(...well, kinda sorta...can't draw a number line on this email) <----l ...-8..-7..-6..-5..-4..-3..-2..-1..0..1..2..3... so any answer less that -4 will make the equation true...let's see pick a number from about....drum roll..please....ding...number -6 so x = -6 and the equation reads -x + 3 > 7 Plug it in to the equation: but remember...! (-1)(x) + 3 > 7 and when x = -6 (-1)(-6) + 3 > 7 complete the operation... negative 1 times negative 6 and ? 6 + 3 > 7 Addition operation 9 > 7 True? I hope so...or all my students are in real big trouble!

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