Question

The equation-3(5v+2)=54 is solved in several steps below for each step choose the reason that best justifies it.

Answer 1

Answer:

1. -3(5v + 2) = 54 ==> given equation

2. -15v - 6 = 54 ==> distributive property of equality

3. -15v - 6 + 6 = 54 + 6 ==> additive property of equality

4. -15v = 60 ==> simplifying

5. -15v/-15 = 60/-15 ==> division property of equality

6. v = -4 ==> simplifying

Step-by-step explanation:

1. this is the equation given

2. distributive property of equality : a(b+c) = a*b + a*c

this is applied in step 2. eg. -3(5v+2) = -3*5v + -3*2= -15v - 6

3. to isolate the variable we must get rid of the -6. to do so we add 6 to both sides hence using the additive property of equality.

4. we then simplify both sides of the equation as we just added 6 to both sides

5. to isolate the variable we have to get rid of the -15 in -15v

v is being multiplied by -15

the inverse of multiplication is division so to get rid of the -15 we divide by -15. what ever we do to one side we must do to the other, hence the division property of equality

6. we then simplify the division

and we are done!