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Inequalities Need help quick
- Thread starter jenna_lea
- Start date
4x-4 >3x+5
I have 4x-4-4> 3x+5-4 What do I do now?
Don't let the inequality sign confuse you. Use all the basic algebra steps that you already know. Just pretend that the inequality symbol is an equal sign.
4x-4 = 3x+5
The only *new* thing to remember is that if you multiply or divide by a negative number, the direction of the inequality symbol reverses.
Also, if you want to get rid of the -4 on the left hand side, you need to add 4 to each side, not subtract.
5>4 but -5<-4.
5 is a higher temperature than 4 but -5 is a lower temperature than -4.
For inequalities, this change can occur if you multiply or divide by a negative value.
If you multiply or divide by a "variable" that could be positive or negative,
you also must account for possible inequality reversals.
The way to avoid those possibilities (if you don't like them) is to only add or subtract with the variable
and multiply and divide by positives only.
Example: 4 -x > 3 so 4 > x+3 so 4-3 >x so x<1
or -x > 3-4 so -x > -1 so x < 1 as we multiply or divide by -1 when we take off the minus sign.
On the first line, we add x to both sides (it's not fully precise to say the x changes sides and sign).
That does not matter if x is + or -.
On the 2nd line we are reversing the inequality, whether or not x is + or -
4x-4 > 3x+5
4x-4+4>3x+5+4 so 4x>3x+9 so 4x-3x>9 so x>9
4x-4>3x+5 so 4x-4x-4>3x-4x+5 so -4>-x+5 so -4-5>-x so -9>-x.
Now you either add x to both sides and add 9 to both sides to get x>9
or multiply or divide both sides by -1 and reverse the inequality to get 9<x.
Just replace the > and < with greater than or equal to and less than or equal to.
5 is a higher temperature than 4 but -5 is a lower temperature than -4.
For inequalities, this change can occur if you multiply or divide by a negative value.
If you multiply or divide by a "variable" that could be positive or negative,
you also must account for possible inequality reversals.
The way to avoid those possibilities (if you don't like them) is to only add or subtract with the variable
and multiply and divide by positives only.
Example: 4 -x > 3 so 4 > x+3 so 4-3 >x so x<1
or -x > 3-4 so -x > -1 so x < 1 as we multiply or divide by -1 when we take off the minus sign.
On the first line, we add x to both sides (it's not fully precise to say the x changes sides and sign).
That does not matter if x is + or -.
On the 2nd line we are reversing the inequality, whether or not x is + or -
4x-4 > 3x+5
4x-4+4>3x+5+4 so 4x>3x+9 so 4x-3x>9 so x>9
4x-4>3x+5 so 4x-4x-4>3x-4x+5 so -4>-x+5 so -4-5>-x so -9>-x.
Now you either add x to both sides and add 9 to both sides to get x>9
or multiply or divide both sides by -1 and reverse the inequality to get 9<x.
Just replace the > and < with greater than or equal to and less than or equal to.