Stumped On Algebra Word Problems?

Question

I am currently taking introductory algebra in my first year of college as a refresher and I'm trying to remember how to do algebra word problems. I suppose my issue is more trying to translate the English into a problem. Some examples...

The sum of twice a number and 1/5 is equal to the difference between three times the number and 4/5. Find the number.

O.K., so I translated that into: 2x + 1/5 = 3X - 4/5

But if that's the number, how would I clear the fractions?

Any help on the process of doing these things would be greatly appreciated. Thanks!

Answer 1

The easy way to clear the fractions is to multiply both sides of the equation by 5.

10x + 1 = 15x - 4

If you solve this, you get x = 1.

Answer 2

1-you want the "X" on only one side so you need to subtract 2x from both sides
2x-2x=0 3x-2x=1
2-then you want to only have the fraction portion of the problem on the other side, so you would need to add 4/5 to both sides so that the x is on the right and the fraction is on the left or visaversa
-4/5+4/5 = 0 1/5+4/5=1
therefore the answer is X=1

Answer 3

2x + 1/5 = 3X - 4/5
1/5+4/5=3x-2x
5/5=x

x=1

Answer 4

8x + 15y + 20z = 783,000 the place x, y, and z are the form of each and every fee ticket bought. We additionally understand that y=2x and that z=y+6000 you already know have 3 equations for 3 unknowns. remedy them in whichever way you opt for and you get that: $8 tickets: 8500 $15 tickets: 17000 $20 tickets: 23000

Answer 5

Just multiply each term by 5.
10x + 1 = 15x - 4
Subtract 10x
1 = 5x - 4
Add 4
5 = 5x
divide by 5
x = 1
If you check this number it works

Answer 6

so, subtract 2x from both sides and add 4/5 to both sides.

Answer 7

Collect like terms and solve for x