Question

practice & problem solving
leveled practice in 8 - 10, find the value of x.

1. lori bought sunglasses and flip - flops at a half - off sale. if she spent a total of $21 on the two items, what was the original price of the sunglasses?

\\(\frac{1}{2}(x + 24)=21\\)
\\(\frac{1}{2}x+24 = 21\\)
\\(\frac{1}{2}x = 18\\)
\\(x = 18\\)
the original price of the sunglasses was

Explanation:

Step1: Expand the equation

Using the distributive property $\frac{1}{2}(x + 24)=21$ becomes $\frac{1}{2}x+\frac{1}{2}\times24 = 21$, so $\frac{1}{2}x + 12=21$. (There was an error in the original work where $\frac{1}{2}\times24$ was wrongly written as 24).

Step2: Isolate the term with $x$

Subtract 12 from both sides of the equation $\frac{1}{2}x+12 - 12=21 - 12$, we get $\frac{1}{2}x=9$.

Step3: Solve for $x$

Multiply both sides of the equation by 2 to get $x = 18$.

Answer:

18