Let’s create a demo for solving a linear equation, focusing on one of the most common forms of linear equations: ax+b=c, where a, b, and c are constants. Solving such an equation involves finding the value of x that makes the equation true.
Example Problem:
Solve the linear equation 3x+4=10.
Step 1: Identify the Equation
Our equation is 3x+4=10, where a=3, b=4, and c=10.
Step 2: Isolate the Variable
To solve for x, we need to get x by itself on one side of the equation. We’ll do this by performing operations that will isolate x.
First, subtract 4 from both sides of the equation to get rid of the constant term on the side with x.
3x+4−4=10−4
Step 3: Simplify
After subtraction, the equation simplifies to:
3x=6
Next, to isolate x, divide both sides of the equation by 3, the coefficient of x.
3x : 3 =6 : 3
Step 4: Solve for x
Solving the equation gives us:
x=2
Conclusion:
The solution to the linear equation 3x+4=10 is x=2.