Solve for $x$.
$9(x+1)=25+x$
Answer (1)
Expand the left side of the equation: 9 ( x + 1 ) = 9 x + 9 .
Subtract x from both sides: 8 x + 9 = 25 .
Subtract 9 from both sides: 8 x = 16 .
Divide both sides by 8 to find the solution: x = 2 .
Explanation
Understanding the Problem We are given the equation 9 ( x + 1 ) = 25 + x and asked to solve for x . We are also given four possible solutions: x = 2 , x = 3 , x = 4 , and x = 5 . We can either solve the equation algebraically or test each of the given solutions to see which one satisfies the equation.
Expanding the Left Side Let's solve the equation algebraically. First, expand the left side of the equation: 9 ( x + 1 ) = 9 x + 9
Rewriting the Equation So the equation becomes: 9 x + 9 = 25 + x
Subtracting x from Both Sides Now, subtract x from both sides of the equation: 9 x − x + 9 = 25 + x − x
Simplifying the Equation This simplifies to: 8 x + 9 = 25
Subtracting 9 from Both Sides Next, subtract 9 from both sides of the equation: 8 x + 9 − 9 = 25 − 9
Simplifying the Equation This simplifies to: 8 x = 16
Dividing by 8 Finally, divide both sides of the equation by 8: 8 8 x = 8 16
Solution This gives us: x = 2
Final Answer Therefore, the solution to the equation 9 ( x + 1 ) = 25 + x is x = 2 .
Examples
Solving linear equations like this is a fundamental skill in algebra. It's used in many real-world situations, such as calculating the cost of items with a fixed price and a variable quantity, determining distances and speeds, or even in financial planning to calculate investments and interest rates. For example, if you're buying multiple items at a store and have a coupon, you might use a similar equation to figure out the final cost.
