7. a) Determine the error, if any, in the solution to this equation. Describe in words, in detail.
-6(2x – 5) = 4x – 2(x + 3)
- 12x + 30 = 4x – 2x – 6
-12x – 12x + 30 = 6x – 12x – 6
30 = -6x - 6
30 + 6 = -6x – 6 + 6
36 = - 6x
36 -6x
-6 -6
-6= x

b) If an error, solve the equation correctly.

5x, -2x and x

Step-by-step explanation:

Given

Expression: 3x

Required

Determine all like terms

Literally, like terms are terms that addition or subtraction operations can easily be performed on.

So, the like terms of 3x are options with integer coefficient of x.

From the list of options, the like terms are 5x, -2x and x

This is so because the factor attached to them are integers just as 3 is to 3x.

Another reason is that, when added or subtracted from 3x, the result is always a single term.

Take for instance:

5x - 3x = 2x

-2x + 3x = x

x + 3x = 4x

Other options such as 3y, 3xy, 3, and 7y are not coefficient because they do not obey the analysis above.

Take for instance

3y + 3x will not result in a single expression.

Same with others