mathematics anyone?

Question

is anyone out there very good at math? i am not. i have to take a summer course in algebra just to get a credit for this year. the one problem i cant figure out is how to solve for 'x' in this problem: abx-b=ab-1. i already know the answer but i dont know how to get there. can you help?

Answer 1

First factor out a common b from the left side:
b(ax-1) = ab-1

Now divide both sides by b:
ax - 1 = a - 1/b

Next add 1 to both sides:
ax = a - 1/b + 1

Now divide both sides by a:
x = 1 - 1/ab + 1/a

If you want of fix the fraction on the right, notice that you can use a common denominator of ab:
x = ab/ab - 1/ab + b/ab

Now group the numerator:
x = (ab - 1 + b)/ab

An alternate way to do this would be:
abx - b = ab - 1

Add b to both sides:
abx = ab - 1 + b

Divide by ab:
x = (ab - 1 + b)/ab

Same result and even quicker...

Either of these answers should be acceptable.

Answer 2

Solve,

abx - b = ab - 1

Rearranging,

abx = ab + b - 1

x = (ab + b - 1)/ab

x = 1 + (b - 1)/ab

Answer 3

abx - b = ab - 1

You want to end up with an equation with just

x =

on one side.

You can eliminate the 2nd term on the left side by adding b to that side and, in order to keep things in balance, you must add b to the other side as well.

abx - b + b = ab + b - 1

or

abx = ab + b - 1

You can eliminate the ab in abx by dividing by ab, remembering to do the same on the other side as well.

abx/ab = (ab + b - 1)/ab

x = (ab + b - 1)/ab

We had to introduce parentheses on the right side because we are dividing the entire right side by ab.

Answer 4

To solve
abx-b=ab-1
first take out the common factor of b on RHS:
b(ax-1) = ab-1
now divide both sides by b:
ax-1 =(ab-1)/b
now add one to both sides:
ax = ((ab-1)/b) + 1
now divide both sides by a:
x = (((ab-1)/b) + 1)/a
yuk! Are you sure you copied the equation correctly?

Answer 5

Given:
abx-b = ab - 1 (Add b to both sides).
abx = ab - 1+ b (Divide by sides by ab).
x = (ab-1+b) / ab (Divide all parts by ab).
x = ab/ab - 1/ab + b/ab
x = 1 - (1+b) / ab

Answer 6

abx-b=ab-1 that implies abx=ab-1+b
that implies x=(ab-1+b)/ab

Answer 7

abx - b=ab - 1
b(ax - 1) = ab - 1
ax - 1 = (ab - 1)/b
ax = a - 1/b + b/b
x = (a - 1/b + 1) / (a)

Answer 8

abx-b=ab-1
abx=ab+b-1
x=(ab+b-1)/ab
x=1+a-(1/ab)

Answer 9

Exactly as explained above... "Solving" for a variable means you want just that variable on one side of the equal sign and everything else on the other...