Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 7: Linear Equations in One Variable

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Answer/Discussion to 1a

*Inverse of add. 5 is sub 5 from both sides

*Inverse of mult. by 6 is div. both sides by 6

If you put 0 back in for y in the original problem you will see that 0 is the solution we are looking for.

Answer/Discussion to 1b

*Get all x terms on one side

*Inverse of sub. 3 is add. 3 to both sides

*Inverse of mult. by 2 is div. both sides by 2

If you put 5 back in for x in the original problem you will see that 5 is the solution we are looking for.

Answer/Discussion to 1c

*Distribute the inner most ( )
*Distribute the outer grouping [ ]

*Get all t terms on one side

*Inverse of mult. by 11 is div. both sides by 11

If you put 8/11 back in for t in the original problem you will see that 8/11 is the solution we are looking for.

Answer/Discussion to 1d

*Mult. both sides by the LCD of 20

*Use dist. property to remove ( )

*Get all x terms on one side

*Inverse of add. 108 is sub. 108

*Inverse of mult. by -51 is div. by -51

If you put 3 back in for x in the original problem you will see that 3 is the solution we are looking for.

Answer/Discussion to 1e

7(x - 3) = 7x + 2

*Use dist. property to remove ( )

*Get all x terms on one side

Since the variable dropped out AND we ended up with a false statement, the answer is no solution.

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