Question

Choose the correct equivalent expression for the given expression:

$\frac{3}{4}$x + 595 + $\frac{5}{2}$x - 121 + x

• A. $\frac{17}{2}$x + 474
• B. $\frac{17}{4}$x + 716
• C. $\frac{17}{2}$x + 716
• D. $\frac{17}{4}$x + 474

Answer 1

The correct option is D $\frac{17}{4}$x + 474

Given expression is:
$\frac{3}{4}$x + 595 + $\frac{5}{2}$x - 121 + x

Let’s add the two linear expressions using properties of expression to calculate total investment.

Using commutative property:
$\frac{3}{4}$x + $\frac{5}{2}$x + x + 595- 121


Using associative property:
= ($\frac{3}{4}$x + $\frac{5}{2}$x + x) + (595 - 121)

= $\frac{3+10+4}{4}$x + 474

= $\frac{17}{4}$x + 474

$\therefore$ Equivalent expression of $\frac{3}{4}\text{x}+595+\frac{5}{2}\text{x}-121+\text{x}$
is $\frac{17}{4}\text{x}+474$.