Question

4x+3(2-x)=8-2x
solve for x, give a reason for each step

Answer 1

you would would PEMDAS (parentheses, exponents, multiplication, division, addition and subtraction) and do it in that order.

so 4x+3(2-x)=8-2x step by step is:

parentheses: (distributive property)
4x+6-3x=8-2x

no exponents.
no multiplication.
no division.

addition:
4x+6-3x=8-2x

4x and -3x have a variable in common, so:

4x-3x+6=8-2x
———->
x+6=8-2x

add 2x to both sides

3x+6=8

now subtract 2 from each side.

3x=2

divide by 3, final answer is x=2/3

Answer 2

4x+3(2-x)=8-2x

Multiply the bracket by 3

(3)(2)=6x

(3)(-x)=-3x

4x+6-3x=8-2x

4x-3x+6=8-2x ( combine like terms)

x+6=8-2x

Move -2x to the other side. Sign changes from -2x to +2x.

x+2x+6=8-2x+2x

x+2x+6=8

3x+6=8

Move +6 to the other side. Sign changes from +6 to -6.

3x+6-6=8-6

3x=2

Divide by 3 for both sides to get x by itself.

3x/3=2/3

Cross out 3 and 3, divide by 3 and then becomes 1*1*x=x

Answer: 2/3