3. Solve for x.


x + 7 < 3x -1


When we transpose x terms to one side and number terms to

the other it would be best to put the x terms on the right, because

there are more x's on the right.


7 + 1 < 3x - x


8 < 2x


Divide both sides by 2


8/2 < x


4 < x


Notice what would happen if we transposed the terms to the

other side.


x + 7 < 3x -1


x - 3x < -7 - 1


-2x < -8


In this case, we have a negative coefficient on the unknown.

When you divide both sides of an inequality by a negative number,

you need to turn the inequality sign around.


x > (-8)/(-2)




x > 4


We see that the rules about changing the direction of an

inequality if you multiply or divide by a negative but keep it

pointing in the same direction if you are multiplying or dividing by a

positive is necessary to keep our results consistent if you do the

problem differently.


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