- Distribute the constant into the parentheses: \(5x + 10 - 3 = 27\).
- Simplify the expression by combining the constant terms: \(5x + 7 = 27\).
- Isolate the term containing the variable by subtracting 7 from both sides: \(5x = 20\).
- Solve for \(x\) by dividing both sides by 5: \(x = \boxed{4}\).
Explanation
- Distributing the Terms
We start with the linear equation \(5(x+2)-3=27\). Our goal is to isolate the variable \(x\) by reversing the order of operations performed on it. First, we apply the distributive property to the term \(5(x+2)\), which gives us \(5x + 10 - 3 = 27\).
- Combining Like Terms
Next, we combine the constant terms on the left side of the equation. We have \(10 - 3 = 7\), so the equation simplifies to \(5x + 7 = 27\).
- Isolating the Variable Term
To isolate the term with \(x\), we subtract 7 from both sides of the equation. This gives us \(5x = 27 - 7\), which simplifies to \(5x = 20\).
- Solving for x
Finally, we solve for \(x\) by dividing both sides of the equation by 5. This gives \(x = \frac{20}{5}\), which simplifies to \(x = 4\). Thus, the solution to the equation is \(x = 4\).
Examples
This type of linear equation is common in everyday scenarios like budgeting. Suppose you have a fixed budget for an activity. If the cost of the activity involves an initial setup fee plus a variable cost per participant (like renting a hall for 2 hours plus an hourly rate for cleaning), you can model this as a linear equation. Solving it helps you determine exactly how many hours or participants your budget can cover, ensuring you stay within your limits.