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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