Question

3|x−7|+10=2|x−7|+2

Answer 1

Are you getting the hang of these?

Answer 2

No not at all i don't understand it

Answer 3

I see. Are you familiar with like terms?

Answer 4

For example, the set of integers such as {...1, 2, 3, 4, 5, 6, 7...} are like terms
The set of terms such as {x, 2x, 3x, 4x...} are like terms
The set of terms such as {|x + 1|, 2|x + 1|, 3|x + 1|, 4|x + 1|...} are like terms.

Answer 5

In general, terms are separated by plus or minus signs. Terms such as 2x are considered one term. 3|x - 7| is considered one term.

Answer 6

When solving algebraic equations, like terms are grouped together to make them easier to work with.

Answer 7

When solving the problem above
we want like terms 3|x - 7| and 2|x - 7| on the same side.
we want like terms 10 and 2 on the same side.

Answer 8

In order to do that, we must either add or subtract certain terms from either side.

Answer 9

In this case subtracting 2|x - 7| from both sides and subtracting 10 from both sides produces:

3|x - 7| - 2|x - 7| = 2 - 10

Answer 10

The next step is a simplification step. 2 - 10 is obviously - 8:

3|x - 7| - 2|x - 7| = -8

Answer 11

Now, for the left side, |x - 7| is treated as a singular variable. You can think of

3|x - 7| - 2|x - 7| in the same way you think of 3y - 2y for the moment.

You know 3y - 2y = y

In the same manner, 3|x - 7| - 2|x - 7| = |x -7|

Answer 12

So that results in

|x - 7| = -8

Answer 13

However, there's a rule that says the absolute value of a number must be positive. In this case,

|x - 7| = -8, the eight is negative, so there is no such x that will make both sides true. So the equation is false.

Answer 14

I think i understand it better ill try some more problems

Answer 15

No solution