Solve the equation, $-(x / 4)=5$, for $x$. Which of the following properties of equality did you apply?
A) Multiplication and subtraction
B) Division
C) Division and addition
D) Multiplication
Answer (1)
Multiply both sides of the equation − ( x /4 ) = 5 by − 4 .
Simplify the left side: ( − 4 ) × − 4 x = x .
Simplify the right side: ( − 4 ) × 5 = − 20 .
The solution is x = − 20 .
Explanation
Understanding the Problem We are given the equation − ( x /4 ) = 5 and asked to solve for x . We need to isolate x on one side of the equation.
Isolating x To isolate x , we can multiply both sides of the equation by − 4 . This will cancel out the − 1/4 factor on the left side.
Performing the Multiplication Multiplying both sides by − 4 , we get: ( − 4 ) × − 4 x = ( − 4 ) × 5 x = − 20
Finding the Solution and Property Therefore, the solution to the equation is x = − 20 . The property of equality used was multiplication.
Examples
Imagine you're sharing a pizza with friends, and you realize that one-quarter of the pizza is missing, represented by − ( x /4 ) , and this missing part equals 5 slices. To find out how many slices the whole pizza ( x ) originally had, you would solve the equation − ( x /4 ) = 5 . Multiplying both sides by -4 tells you that the whole pizza had -20 slices. In this context, the negative sign indicates something is missing, so the pizza originally had 20 slices, but 5 are missing.
