Expert: Scott A Wilson - 5/29/2010

Question
I have been working on these questions for 5 weeks and I am no where near getting them right.

Solve the inequality and graph the solution:

1. 4x + 13 < 41

2.-5x - 11 > 29

3. 8x + 6 + x > (or equal to) 3 + 5x + 19

4. -x + 2 + 13x > (or equal to) -5 + 5x + 49

5. 7x + 3 > 3( 2x + 1 ) - x + 5

Please help I am desperate.

Answer
1. 4x + 13 = 41
Subtract 13 from both sides.
This gives 4x < 28.
Divide both sides by 4, given x < 7.
That means all points on the number line to the left of 7.
Note that 7 is not included.

2. Add 11 to both sides.
Divide both sides by 5.
This will gives -5x < -40.
This is the same as 5x > 40.
Divide both sides by 5, and you're done.

3.  8x + 6 + x >= 3 + 5x + 19
This equation becomes, combining terms, 9x + 6 >= 5x + 22.
Add -5x-6 to both sides.
There should now be only x terms on the left and only constants on the right.

Once this has been done, divide both sides by 4.
The answer should have a lower limit of an integer n.
The answer should also be x >= n.

4. -x + 2 + 13x >= -5 + 5x + 49
Combine like terms into 12x + 2 >= 5x + 44.
Add -2-5x to both sides to get only x on the left and only constants on the right.
Divide both sides by 7 go get the value at the end of the line for x.
The values are at this point and all values greater or equal to this integer.

5. 7x + 3 > 3(2x+1) - x + 5
Work this out to 7x + 3 > 6x + 3 - x + 5.
Terms can be combined to get 7x + 3 > 5x + 8.
Adding -3 -5x to both sides gives 2x > 5.
Dividing by 2 gives x > 5/2.