We are given the linear equation 2x minus 5 equals 13. Our goal is to find the value of x that makes this equation true. This is a linear equation in one variable, meaning it has only one unknown value, x, and the highest power of x is 1.
Think of an equation as a balanced scale. The left side, 2x minus 5, must equal the right side, 13. To maintain this balance, whatever operation we perform on one side, we must also perform on the other side. This fundamental principle will guide us through solving the equation.
Our first step is to eliminate the minus 5 on the left side. To do this, we add 5 to both sides of the equation. On the left side, we have 2x minus 5 plus 5, and on the right side, we have 13 plus 5. When we simplify both sides, the minus 5 and plus 5 on the left cancel out, leaving us with 2x equals 18.
Now we need to isolate x by eliminating the coefficient 2. We do this by dividing both sides of the equation by 2. On the left side, we have 2x divided by 2, and on the right side, we have 18 divided by 2. When we simplify, the 2s on the left cancel out, leaving just x, and on the right, 18 divided by 2 equals 9. Therefore, x equals 9.
To confirm our solution is correct, we substitute x equals 9 back into the original equation. We replace every x with 9, giving us 2 times 9 minus 5 equals 13. Simplifying the left side, 2 times 9 is 18, and 18 minus 5 is 13. Since both sides of the equation equal 13, our solution x equals 9 is verified as correct.
Let's summarize the complete solution process. Step 1: We start with the original equation, 2x minus 5 equals 13. Step 2: We add 5 to both sides to get 2x minus 5 plus 5 equals 13 plus 5. Step 3: We simplify to 2x equals 18. Step 4: We divide both sides by 2 to get 2x divided by 2 equals 18 divided by 2. Step 5: We simplify to find that x equals 9. This is our final solution, which we have verified is correct.