Question

5 juanita says that 3\frac{5}{4}d - (2)(1.5) and 2\frac{7}{4}d - (5)(1.05) are equivalent. is juanita correct? explain your reasoning.

Explanation:

Step1: Simplify the first expression

First, calculate the product inside the parentheses for the first expression \(3.5[4d - (2)(1.5)]\). First, compute \((2)(1.5)=3\). Then the expression inside the brackets becomes \(4d - 3\). Now multiply by \(3.5\): \(3.5\times4d-3.5\times3 = 14d - 10.5\)

Step2: Simplify the second expression

Now, simplify the second expression \(2[7d - (5)(1.05)]\). First, calculate \((5)(1.05) = 5.25\). Then the expression inside the brackets is \(7d - 5.25\). Multiply by \(2\): \(2\times7d-2\times5.25=14d - 10.5\)

Step3: Compare the two simplified expressions

Both expressions simplify to \(14d - 10.5\), so they are equivalent.

Answer:

Juanita is correct because both expressions simplify to \(14d - 10.5\) (after simplifying the first expression \(3.5[4d - (2)(1.5)]\) to \(14d - 10.5\) and the second expression \(2[7d - (5)(1.05)]\) to \(14d - 10.5\), showing they are equivalent).