Solving One-Step Equations

Understanding how to solve one-step equations is one of the fundamental skills in algebra. This concept is important because it forms the basis for solving more complex equations and helps to understand how variables and constants interact within an equation. In this explanation, we will dive into the technique and logic behind solving one-step equations, using simple English for clarity.

What is a one step equation?

A one-step equation is an equation that you can solve with just one operation, such as addition, subtraction, multiplication, or division. It usually involves one variable (often represented by a letter such as x or y) that you have to solve for.

Here are some examples of one-step equations:

• x + 5 = 12
• y - 3 = 10
• 2z = 16
• w/4 = 3

Steps to solve one-step equations

The goal of solving one-step equations is to isolate the variable on one side of the equation. This means that you need to perform an operation that gets the variable by itself. To do this, you need to use the inverse operation to cancel out the number with the variable.

Solving by addition

When you have an equation in which a number is subtracted from the variable, such as y - 3 = 8, you can solve it by adding the same number to both sides of the equation. This is because addition is the inverse operation of subtraction.

Equation: y – 3 = 8
Add 3 to both sides to solve for y:
y – 3 + 3 = 8 + 3

At this point the equation becomes:
y = 11

The logic here is that by adding 3 to -3, you cancel it out, and y is left alone on one side of the equation.

Let's look at this visually:

By representing this equation visually, you can easily see that adding 3 to both y and 8 will maintain balance.

Solving by subtraction

If a number is added to the variable, such as in the equation x + 7 = 15, you will solve it by subtracting that number from both sides. Subtraction is the inverse of addition.

Equation: x + 7 = 15
Subtract 7 from both sides to solve for x:
x + 7 - 7 = 15 - 7

Thus, the equation simplifies to:
x = 8

In this case, subtracting 7 takes it off the left side of the equation, and x falls apart.

Visual example:

Balance is maintained by ensuring equality on both sides through subtraction.

Solving by multiplication

When you encounter a one-step equation like (a/4) = 2, you can solve it by multiplying. Multiplication is the inverse operation of division.

Equation: a/4 = 2
Multiply both sides by 4 to solve for a:
(a/4) * 4 = 2 * 4

The result is this:
A = 8

When you multiply a fraction by its denominator, you undo the quotient on the left side, and isolate the variable.

Visual example:

Solving by division

Finally, when a variable is multiplied by a number, such as in the equation 5b = 45, you can solve it using division. Division cancels out the process of multiplication.

Equation: 5b = 45
Divide both sides by 5 to find the value of b:
5b / 5 = 45 / 5

The simplification of which is as follows:
b = 9

Here, dividing by the coefficient of b gives you the value of b. A visual example could be:

Practice problems

Now that you've learned the principles of solving one-step equations, try solving these practice problems. Even though they look different, the steps are the same. Remember to use inverse operations.

• x + 9 = 16
• y - 5 = 12
• 3z = 21
• w/5 = 4

By practicing these, you will develop a more intuitive understanding of algebra and the role of each operation in solving equations.

Conclusion

Solving one-step equations is an essential skill in math. It lays the foundation for understanding algebra and equips you with the ability to handle more complex equations. Always remember to use inverse operations to isolate the variable, while maintaining the balance of the equation. With practice and patience, solving these equations will become second nature to you.

Continue practicing solving one-step equations and try explaining the process to others to further solidify your understanding.

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