Solving Equations, Inequalities, Word Problems and Absolute Values

1. Solve for x:
0.05(x+20)=0.1x-0.5

2. Solve for y, given that x = -3
3xy-2x=-12

3. Line 1 is described by the equation 3y-2x = -3. Line 2 goes through the origin and intersects line 1 at x =6. What equation describes line 2?

4. Solve for x:
l x-1/2 l = 3x/2-3/4

5. Bob received $14,000 inheritance and divided it between a mutual fund that yielded a yearly return of 5% and a 1-year CD that paid 3.5% annually. If his total earnings for the year on this investment was $640, how much did he invest in each of these two funds?

6. Solve the following compound inequality for x:
-1<2x-7<43 AND 10>4-3(x+3)>-20

7. Solve the compound inequality for Y:
0<2y+8<12 OR 3>2(5-y)+3>-17

8. A car dealer offers you a choice of 0% financing for 60 months or $2500 cash back on a new vehicle. You have a pre-approved 60-month loan you can use from your credit union at a 4% interest rate. If the monthly payments at 0% are $16.67 per $1000 financed, and the monthly payments at 4% are $18.41 per $1000 financed, what is the range of new car prices for which the cash back option will cost you less? For what range of car prices should you take the 0% financing?

9. How do I solve the following system of equations:
3y+1=2(x+8) AND 3Y+5=2X-4

10. How do I solve the following system of equations:
5x+3y=5(4-x) AND 2x-5y=-(y+11)/2

11. How do I solve for x:
l2x+3l = lx+1/2l

12. What is the equation of a line that passes through the points (1,2) and (5,4)?

13. You have a jug of 40% antifreeze solution in your garage, and you just bought a new container of 100% antifreeze from the auto parts store. You need to mix up 1 gallon of 50% antifreeze for your car's radiator. How much of each of the two solutions do you need to use?

14. Line 1 passes through the origin (3,1). Line 2 has a slope of -2/3 and passes through the point (-1,5). Where do these two lines intersect?

15. Line 1 crosses the y-axis at y=5 and passes through the point (2,1). Line 2 is perpendicular to Line 1 and crosses the x axis at x=3. What is the equation for line 2?