How do you solve this literal equation for x? ax+b=cx+d ?

Question

can you show me step by step?

Answer 1

ah am too late; ok lets get started;
ax+b=cx+d

ax-cx = d - b;
Factor x
x(a - c) = d -b
x = ( d -b ) / (a - c)

Thats all.
Good Luck.

Answer 2

Question:
|ax+b| = cx + d

how to show sometimes the above has 2 roots, sometimes 1 root and sometimes no roots. Hopelessly lost on how to start...

so far I have
1. ax+b = cx+d
2. -ax-b = cx+d

using 1.
x = (d-b)/(a-c)

using 2.
x= -(d+b)/(a-c)

I think your teacher is looking for values of a, b, c and that will give 1 root, 2 roots or no roots.

For example if a = 1, d = 1 and b = c = 0 then the equation becomes

|x| = 1

In this situation x can be 1 or -1 and thus this is a situation with 2 roots.

Can you find choices for a, b, c and that will give no roots? 1 root?

Penny

Answer 3

The idea is to group all the x terms together on one side and all the non-x terms on the other. Then divide as necessary to get to just x.

Original equation:
ax + b = cx + d

Start by subtracting cx from both sides:
ax - cx + b = d

Now subtract b from both sides:
ax - cx = d - b

Now factor out a common x term:
(a - c)x = d - b

Now divide both sides by a - c:
x = (d - b) / (a - c)

Answer 4

ax + b = cx + d
ax - cx + b = d (subtracted cx from both sides. (Put all the xs on one side of the equation))

ax - cx = d - b (subtracted all constants from the x side.)

(a - c) x = d - b (factored out the x.)
x = (d-b) / (a-c)

Solving for x just means getting all the other garbage on the other side of the equals sign from x.

Answer 5

putting like terms together the equation becomes:
ax-cx=b+d
Taking the common factor x out on the right side of the equation we have:
x(a-c)=b+d
Dividing both sides by a-c will give you the value of x
x(a-c)/(a-c)=(b+d)/(a-c)
x=(b+d)/a-c

Answer 6

A visual of the step by step instructions on solving for a letter:
http://regentsprep.org/Regents/Math/formulas/litless.htm

Answer 7

ax-cx = d - b;
Factor x
x(a - c) = d -b
x = ( d -b ) / (a - c)

Answer 8

ax+b=cx+d
(a-c)x=d-b
x=(d-b)/(a-c)

Answer 9

x = (d-b)/(a-c)