Which two expressions are equivalent? A. {:[4(2+x)],[4*2+4*x]:} B. {:[4+2+x],[(4+2)+x]:} C. {:[4*x+2],[4*(x+2)]:} D. {:[4÷(2-x)],[4-2÷x]:}

Question

Bytelearn · Accepted Answer

Analyze option A: First, let's analyze option A: 4(2+∣x∣). This expression means 4 times the sum of 2 and the absolute value of x. To simplify, we distribute the 4 across the terms inside the parentheses. Calculation: 4(2) + 4(∣x∣) = 8 + 4∣x∣Look at option B: Now let's look at option B, which is presented in a matrix form. This is likely a typographical error, as expressions are not typically presented in a matrix. However, we can interpret the middle row as the intended expression: (4+2)+x. Simplifying this expression, we combine the like terms. Calculation: (4+2)+x = 6+xExamine option C: Next, we examine option C: 4*x+2. This expression is simply the product of 4 and x, plus 2. There is no distribution or simplification needed. Calculation: 4*x + 2 remains as it is.Consider option D: Option D is 4÷(2-x). This expression involves division and cannot be simplified to a form similar to the previous options without further information about x. Calculation: 4÷(2-x) remains as it is.Analyze expression 4*(x+2): Finally, we have the expression 4*(x+2). This expression means 4 times the sum of x and 2. To simplify, we distribute the 4 across the terms inside the parentheses. Calculation: 4*(x) + 4*(2) = 4x + 8Now, let's compare the simplified forms of all options to find the equivalent expressions: A: 8 + 4∣x∣ B: 6+x C: 4x+2 D: 4÷(2-x) E: 4x+8 We can see that none of the options are equivalent to each other. Each expression has different terms or operations involved.

Which two expressions are equivalent? $\newline$ A. $4(2+x) \\ \quad 4 \cdot 2 + 4 \cdot x$ $\newline$ B. $4+2+x \\ \quad (4+2)+x$ $\newline$ C. $4 \cdot x+2 \\ \quad 4 \cdot (x+2)$ $\newline$ D. $4 \div(2-x) \\ \quad 4 - 2 \div x$

Full solution

More problems from Simplify variable expressions using properties

Related topics