Solve $x+2+\frac{x}{2}+7+x=24$
Answer (1)
Combine like terms: x + 2 + 2 x + 7 + x = 24 becomes 2 5 x + 9 = 24 .
Isolate the x term: Subtract 9 from both sides to get 2 5 x = 15 .
Solve for x: Multiply both sides by 5 2 to get x = 5 30 .
Simplify: x = 6 , so the final answer is 6 .
Explanation
Understanding the Problem We are given the equation x + 2 + 2 x + 7 + x = 24 . Our goal is to solve for x .
Combining Like Terms First, let's combine the like terms on the left side of the equation. We have x + x + 2 x + 2 + 7 = 24 . Combining the x terms, we get 2 x + 2 x . To add these, we can rewrite 2 x as 2 4 x . So, we have 2 4 x + 2 x = 2 5 x .
Simplifying the Equation Now, let's combine the constant terms: 2 + 7 = 9 . So, our equation becomes 2 5 x + 9 = 24 .
Isolating the x Term Next, we want to isolate the term with x . To do this, we subtract 9 from both sides of the equation: 2 5 x + 9 − 9 = 24 − 9 , which simplifies to 2 5 x = 15 .
Solving for x Now, we want to solve for x . To do this, we multiply both sides of the equation by 5 2 : 5 2 × 2 5 x = 15 × 5 2 . This simplifies to x = 5 30 .
Final Answer Finally, we simplify the fraction: x = 6 . Therefore, the solution to the equation is x = 6 .
Examples
Imagine you're baking a cake and need to adjust the recipe. If you know the total amount of flour needed and have an equation representing how much flour is in each ingredient, solving for 'x' (like in our problem) helps you determine the exact quantity of a specific ingredient to add. This ensures your cake turns out perfectly! Similarly, in budgeting, if you have a total budget and know the costs of some items, solving a linear equation helps you find out how much you can spend on other items.
