We are given a linear equation in one variable: 2x minus 5 equals 14. Our goal is to find the value of x that makes this equation true.
An equation is like a balanced scale. Whatever we do to one side, we must do to the other side to maintain balance. Here, 2x minus 5 on the left equals 14 on the right.
To isolate the term with x, we add 5 to both sides of the equation. On the left side, negative 5 plus 5 cancels out, leaving us with 2x. On the right side, 14 plus 5 equals 19.
Now to solve for x, we divide both sides by 2. On the left side, 2 divided by 2 cancels out, leaving just x. On the right side, 19 divided by 2 equals 9.5.
Let's verify our solution by substituting x equals 9.5 back into the original equation. We get 2 times 9.5 minus 5 equals 14. Simplifying, 19 minus 5 equals 14. Since both sides equal 14, our solution is correct.
Here's a summary of the steps to solve linear equations in one variable. First, identify the equation structure. Second, isolate the term with the variable using addition or subtraction. Third, solve for the variable using multiplication or division. Finally, verify your solution by substituting it back into the original equation.