Consider the equation.
[tex]$4(p x+1)=64$[/tex]
The value of [tex]$x$[/tex] in terms of [tex]$p$[/tex] is [ ].
The value of [tex]$x$[/tex] when [tex]$p$[/tex] is -5 is [ ].
Answer (1)
First, distribute the constant in the equation: 4 p x + 4 = 64 .
Then, isolate the term with x : 4 p x = 60 .
Next, solve for x in terms of p : x = p 15 .
Finally, substitute p = − 5 to find x = − 5 15 = − 3 .
Explanation
Understanding the Problem We are given the equation 4 ( p x + 1 ) = 64 and we need to find the value of x in terms of p , and then find the value of x when p = − 5 .
Distributing the Constant First, let's solve the equation for x in terms of p . We start by distributing the 4 on the left side of the equation: 4 ( p x + 1 ) = 64
4 p x + 4 = 64
Isolating the Term with x Next, we subtract 4 from both sides of the equation: 4 p x + 4 − 4 = 64 − 4
4 p x = 60
Solving for x in terms of p Now, we divide both sides by 4 p to solve for x : 4 p 4 p x = 4 p 60
x = p 15
Finding x when p = -5 Now that we have x in terms of p , we can find the value of x when p = − 5 . We substitute p = − 5 into the equation: x = − 5 15
x = − 3
Examples
Understanding how to solve for a variable in terms of another is crucial in many real-world applications. For example, in physics, you might want to express the velocity of an object in terms of time and acceleration. If you have the equation d = v 0 t + 2 1 a t 2 , where d is distance, v 0 is initial velocity, a is acceleration, and t is time, you can solve for a in terms of the other variables to understand how acceleration affects the distance traveled. This skill is also useful in economics, where you might express the price of a product in terms of supply and demand.
