Question

Simplify the expression \[(4x + 8) + ( - 6x)\]. Explain how the associative and commutative properties were used to solve the expression?

Answer 1

Hint: In the given question we have been asked to simplify \[(4x + 8) + ( - 6x)\] and with this you have to explain how you used the associative and commutative properties. For this first you should recall what the meaning of associative as well as commutative is and recall what were the properties or rules of associative and commutative. So associative means grouping of numbers or variables in algebra you can re-group numbers or variables and you will always arrive at the same answer whereas commutative means you can move the given numbers or the variables in algebra around and still arrive at the same answer. N

Complete step-by-step answer:
In the given question we have \[(4x + 8) + ( - 6x)\] term which we have to simply solve but we have to mention the associative and commutative properties.
Now associative law of addition is \[a + (b + c) = (a + b) + c\]and commutative law of addition is \[a + b = b + a\]
Now we will solve the given equation step wise i.e.
\[1)\]We will use distribution property to change
\[ + \times ( - 6x)\]to \[ - 6x\]we get \[( + 4x + 8) + - 6x\]
\[2)\]Now remove the parentheses of \[( + 4x + 8)\] we get \[ + 4x + 8 + - 6x\]
\[3)\]Using commutative property to move \[ - 6x\]and \[ + 8\]we get \[ + 4x - 6x + 8\]
\[4)\]Using associative property to group \[ + 4x - 6x\] we get \[( + 4x - 6x) + 8\]
\[5)\]Now using algebraic addition to solve \[( + 4x - 6x)\]we get \[( + 4x - 6x) + 8 = - 2x + 8\]
\[6)\]Now simply taking \[ - 2\] common from the terms we get \[ - 2\left\{ {\dfrac{{ - 2x}}{{ - 2}} + \dfrac{8}{{ - 2}}} \right\} = - 2(x - 4)\]
Hence, \[ - 2(x - 4)\] this is the simplified term.
So, the correct answer is “ \[ - 2(x - 4)\]”.

Note: Here you should know what are the associative and commutative properties also learn all the different laws like associative law of addition, multiplication and commutative law of addition, multiplication. Also learn what are the distributive law, cancellation law of addition and cancellation law of multiplication.