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 Question from Lordyne, a student: How do I work this math problem? 18x - 5 = 3(6x - 2)

Hello Lordyne,
In this math problem, we want to solve for x, that is find all numbers x so that 18x - 5 = 3(6x - 2). We will need to distribute first, then combine like terms, and solve for x.
We will do a similar problem for you, so you can see the process, and use it to solve your problem.

5(2x - 3) = 15x - 5
10x - 15 = 15x - 5
-15 + 5 = 15x - 10x
-10 = 5x
-2 = x

This problem has a solution, x = -2.

But what if the problem were 3(2x - 3) = 6x - 5? Distributing first, then combine like terms, and solving for x results in

-9 = -5 which is clearly impossible.

The conclusion is that there is no x such that 3(2x - 3) = 6x - 5, because if there were then -9 would equal -5.

Use all of this information to help solve your problem.
Pam and Penny

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