Use the properties of operations to determine if each pair of expressions is equivalent 1/2(4-2x); 2-2x

Using the properties of operations the given pair of expressions are not equivalentSolution:Given that, we have to use the properties of operations to determine if each pair of expressions is equivalentAnd the two expressions are:[tex]\frac{1}{2}(4-2 x) \text { and } 2-2 x[/tex]Now, we know that, there are four (4) basic properties of operations:Commutative, Associative, Distributive and Identity. These properties only apply to the operations of addition and multiplication.So, if we observe we can apply distributive property on 1st expressionThe distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.[tex]\begin{array}{l}{\frac{1}{2}(4-2 x) \rightarrow \frac{1}{2}(4)-\frac{1}{2}(2 x)} \\\\ {\rightarrow 2-x}\end{array}[/tex]Here the resulting expression is 2 – x and it is not equivalent to 2 – 2xHence, the given two expressions are not equal.