- Simplify the expression on both sides of the equation: \(5x - 11 = x + 10\).
- Isolate the variable terms on one side: \(4x = 21\).
- Solve for \(x\) by dividing: \(x = \frac{21}{4}\).
- Final answer: \(\boxed{\frac{21}{4}}\).
Explanation
- Analyzing the equation
The given equation is \(-4 + 5x - 7 = 10 + 3x - 2x\). To find the value of \(x\), we need to simplify both sides of the equation by combining like terms and then isolate the variable \(x\).
- Simplifying both sides
Starting with the left side, we combine the constant terms \(-4\) and \(-7\):
\[5x - 4 - 7 = 5x - 11\]
On the right side, we combine the terms involving \(x\), which are \(3x\) and \(-2x\):
\[10 + 3x - 2x = 10 + x\]
Now the equation is simplified to:
\[5x - 11 = x + 10\]
- Isolating the variable x
To isolate the variable \(x\), we first subtract \(x\) from both sides of the equation:
\[5x - x - 11 = 10\]
\[4x - 11 = 10\]
Next, we add \(11\) to both sides to move the constant term to the right side:
\[4x = 10 + 11\]
\[4x = 21\]
- Solving for x
Finally, divide both sides by \(4\) to solve for \(x\):
\[x = \frac{21}{4}\]
Comparing this to the provided options, it matches the first option. Therefore, the correct solution is \(x = \frac{21}{4}\).
Examples
Solving linear equations is a fundamental skill in many real-life applications. For example, if you are planning a budget for a party, you might have a fixed cost for the venue and a variable cost per person (like food). If you know the total budget and the costs, you can set up a linear equation to determine the maximum number of guests you can invite. This ensures your event stays within financial constraints while allowing for optimal planning.