Solving One-Step Equations

One-step equations are the simplest type of algebraic equations to solve. They involve only one mathematical operation and can be solved in a single step using inverse operations. The goal is to isolate the variable on one side of the equation to determine its value.

Inverse operations are operations that undo each other. Addition and subtraction are inverse operations, as are multiplication and division. To solve a one-step equation, you perform the inverse operation on both sides of the equation to maintain balance. Whatever you do to one side, you must do to the other.

For example, consider the equation x + 5 = 12. To isolate x, we need to undo the addition of 5. The inverse operation of addition is subtraction, so we subtract 5 from both sides of the equation: x + 5 - 5 = 12 - 5. This simplifies to x = 7. Therefore, the solution to the equation is x = 7.

Another example is the equation y - 3 = 8. To isolate y, we need to undo the subtraction of 3. The inverse operation of subtraction is addition, so we add 3 to both sides of the equation: y - 3 + 3 = 8 + 3. This simplifies to y = 11. Therefore, the solution to the equation is y = 11.

Now let's look at multiplication and division. Consider the equation 3z = 15. This means 3 times z equals 15. To isolate z, we need to undo the multiplication by 3. The inverse operation of multiplication is division, so we divide both sides of the equation by 3: 3z / 3 = 15 / 3. This simplifies to z = 5. Therefore, the solution to the equation is z = 5.

Finally, consider the equation a / 4 = 6. To isolate a, we need to undo the division by 4. The inverse operation of division is multiplication, so we multiply both sides of the equation by 4: (a / 4) * 4 = 6 * 4. This simplifies to a = 24. Therefore, the solution to the equation is a = 24.