give the reason to justify each step
a. 4c+3(2+c)=4c+6+3c
b. =4c+3c+6
c. =(4c+3c)+6
d. =(4+3)c+6
e =7c+6
a. In this step, we distribute the 3 into the parentheses by multiplying it to both terms inside the parentheses: 3(2+c) = 3*2 + 3*c = 6 + 3c. This is justified by the distributive property of multiplication.
b. In this step, we combine like terms by adding the terms with the same variable. We have 4c + 6 + 3c, and since both terms have 'c', we can combine them by adding their coefficients: 4c + 3c = 7c. The '6' remains unchanged since it does not have a variable term. This step is justified by the associative property of addition.
c. In this step, we use the associative property of addition. We group the terms with 'c' together by adding 4c and 3c in parentheses: (4c + 3c) + 6. This step does not change the value of the expression, but it helps us visually see the terms that are being combined.
d. In this step, we simplify the expression by factorizing 'c' as a common factor. We have (4 + 3)c + 6, and since 'c' is common to both terms within the parentheses, we can factor it out: (4 + 3)c = 7c. The '6' remains unchanged.
e. In this final step, we have simplified the expression to 7c + 6 by combining like terms. The '7c' comes from the factored term in the previous step, and the '6' remains unchanged. The expression is in its simplest form and cannot be simplified further.