What is the solution to this equation?
$3 x-5+2 x=25$
A. $x=20$
B. $x=4$
C. $x=6$
D. $x=30$
Answer (1)
Combine like terms: 3 x + 2 x − 5 = 25 becomes 5 x − 5 = 25 .
Add 5 to both sides: 5 x = 30 .
Divide by 5: x = 5 30 .
The solution is x = 6 .
Explanation
Understanding the Problem We are given the equation 3 x − 5 + 2 x = 25 and we want to find the value of x that satisfies this equation.
Combining Like Terms First, we combine the like terms on the left side of the equation. The like terms are the terms with x , which are 3 x and 2 x . Combining these gives us 3 x + 2 x = 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 add 5 to both sides of the equation: 5 x − 5 + 5 = 25 + 5 . This simplifies to 5 x = 30 .
Solving for x Finally, we solve for x by dividing both sides of the equation by the coefficient of x , which is 5: 5 5 x = 5 30 . This gives us x = 6 .
Final Answer Therefore, the solution to the equation 3 x − 5 + 2 x = 25 is x = 6 .
Examples
Imagine you are buying items at a store. You want to buy three of one item and two of another. After using a $5 off coupon, your total is $25. This equation helps you determine the price of each item if you know the total cost and the discount.
