Question

Please help I need to pass this lesson

Answer 1

It would be 3x+24=42
It would be that way because you distribute the 3 outside of the parentheses
3(x+8)=42
3x+(8)(3)=42
3x+24=42

Answer 2

No, No, No, Yes, Yes, Yes

Explanation:

You want to identify the possible first steps in solving 3(x +8) = 42.

First step

If the distributive property is used as the first step in solving this equation, you get ...

(3·x) +(3·8) = 42 . . . . . . multiplier of 3 is indicated as distributed

3x +24 = 42 . . . . . . . . . multiplier of 3 is actually distributed

Arguably, either of these equations is the result of taking the first step toward a solution of the equation.

Alternate first step

Dividing both sides of the equation by 3 is another way a first step might be taken:

(x +8) = 42/3 . . . . . . division by 3 is indicated

x + 8 = 14 . . . . . . . . . division by 3 is actually done

Consequently, we consider any of the equations in bold above to be possible first steps in the solution. The expressions can be sorted as ...

No, No, No, Yes, Yes, Yes

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Additional comment

The lesson is about the distributive property, so you might get pushback on the idea that x+8=14 is a legitimate first step in the solution. It is actually a very good first step, as it makes the numbers smaller, taking less mental effort to do the next step.

In short, there's not a lot of benefit in multiplying by 3, only to have to divide by 3 to get the solution in the end.