Answer:
Solving linear equations involves isolating the variable to find its value. Here are the general steps to solve a linear equation:
1. **Write down the equation**: Ensure it is in the form \(ax + b = c\), where \(a\), \(b\), and \(c\) are constants and \(x\) is the variable you're solving for.
2. **Simplify both sides of the equation**: Combine like terms to make the equation easier to work with.
3. **Isolate the variable**: Use inverse operations to move all terms containing the variable to one side of the equation and all constants to the other side. Remember that you must perform the same operation on both sides to keep the equation balanced.
4. **Solve for the variable**: Once the variable is isolated on one side of the equation, you should have an equation in the form \(x = \text{{some value}}\). This value is the solution to the equation.
5. **Check your solution**: Substitute the found value back into the original equation to ensure it satisfies the equation.
Here's an example to illustrate these steps:
Let's solve the equation: \(3x - 7 = 11\)
1. **Write down the equation**: \(3x - 7 = 11\)
2. **Simplify**: No simplification needed in this case.
3. **Isolate the variable**:
Add 7 to both sides to move the constant term to the other side of the equation:
\[3x - 7 + 7 = 11 + 7\]
\[3x = 18\]
4. **Solve for the variable**:
Divide both sides by 3 to isolate \(x\):
\[\frac{3x}{3} = \frac{18}{3}\]
\[x = 6\]
5. **Check your solution**:
Substitute \(x = 6\) back into the original equation:
\[3(6) - 7 = 11\]
\[18 - 7 = 11\]
\[11 = 11\]
The left side equals the right side, so the solution is correct.
That's how you solve a linear equation. The process remains the same regardless of the coefficients or constants involved.
Step-by-step explanation:
