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

or

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)

 

or

 

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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