A linear equation is an equation where the variable appears to the first power. The general form is ax plus b equals c. Today we'll solve the specific equation x plus 101 equals 123. Our goal is to find the value of x that makes this equation true.
Think of equations as balanced scales. Both sides must be equal for the equation to be true. In our equation x plus 101 equals 123, the left side and right side are balanced. Whatever operation we perform on one side, we must perform on the other side to maintain this balance. This is the fundamental principle of solving equations.
Our goal is to isolate x, which means getting x by itself on one side of the equation. Since x is added to 101, we can undo this addition by subtracting 101 from both sides. This gives us x plus 101 minus 101 equals 123 minus 101. The plus 101 and minus 101 cancel out on the left side, leaving us with x equals 123 minus 101.
Let's work through the complete solution step by step. We have x plus 101 minus 101 equals 123 minus 101. This simplifies to x equals 123 minus 101. Calculating 123 minus 101 gives us 22, so x equals 22. Now let's verify our answer by substituting x equals 22 back into the original equation. 22 plus 101 equals 123, and 123 equals 123. Our solution is correct!
There are multiple ways to solve the same linear equation. Method one uses the subtraction approach we just learned. Method two uses mental math by asking what number plus 101 equals 123. Method three explicitly uses inverse operations, knowing that subtraction undoes addition. All three methods lead to the same answer: x equals 22. This shows that mathematics offers flexibility in problem-solving approaches.