What value of $x$ satisfies the equation $2x + 5 + 3x = 25$?
A. $x=3 \frac{1}{3}$
B. $x=4$
C. $x=5$
D. $x=20
Answer (1)
Combine like terms: 2 x + 3 x + 5 = 25 becomes 5 x + 5 = 25 .
Subtract 5 from both sides: 5 x = 20 .
Divide both sides by 5: x = 4 .
The value of x that satisfies the equation is 4 .
Explanation
Understanding the equation Let's solve the equation step-by-step. The equation is 2 x + 5 + 3 x = 25 . Our goal is to isolate x on one side of the equation.
Combining like terms First, we combine the like terms on the left side of the equation. We have 2 x and 3 x , which combine to 5 x . So the equation becomes 5 x + 5 = 25 .
Isolating the x term Next, we want to isolate the term with x . To do this, we subtract 5 from both sides of the equation: 5 x + 5 − 5 = 25 − 5 , which simplifies to 5 x = 20 .
Solving for x Now, we want to solve for x . To do this, we divide both sides of the equation by the coefficient of x , which is 5: 5 5 x = 5 20 , which simplifies to x = 4 .
Checking the answer Finally, we can check our answer by substituting it back into the original equation: 2 ( 4 ) + 5 + 3 ( 4 ) = 8 + 5 + 12 = 13 + 12 = 25 . Since this is true, our answer is correct.
Examples
Imagine you are buying tickets to a concert. Each ticket costs $2, and there is a service fee of $5. If you have a friend who is also buying tickets, the total cost for both of you is $25. This equation helps you determine how many tickets each of you is buying. By solving for x, you can find the number of tickets you and your friend are purchasing.
