Solving One-Step Equations

A one-step equation is an algebraic equation that takes just one step to solve. Your goal is to find the value of the unknown variable (like $x$ or $y$) by getting it all by itself on one side of the equal sign.

To do this, we use inverse operations. Inverse operations are simply opposite operations that "undo" each other:

• The inverse of addition is subtraction.
• The inverse of subtraction is addition.
• The inverse of multiplication is division.
• The inverse of division is multiplication.

Remember the Golden Rule of Algebra: Whatever you do to one side of the equation, you must do the exact same thing to the other side to keep it balanced!

Addition and Subtraction Equations

If a number is being added to your variable, subtract that number from both sides. If a number is being subtracted, add it to both sides.

Example 1: Solve $x + 7 = 15$

1. Identify the operation: $7$ is being added to $x$.
2. Use the inverse operation: Subtract $7$ from both sides. $x + 7 - 7 = 15 - 7$ $x = 8$

Example 2: Solve $y - 5 = 12$

1. Identify the operation: $5$ is being subtracted from $y$.
2. Use the inverse operation: Add $5$ to both sides. $y - 5 + 5 = 12 + 5$ $y = 17$

Multiplication and Division Equations

When a number is right next to a variable (like $3x$), it means they are being multiplied. To undo this, you divide. If the variable is over a number as a fraction (like $\frac{y}{4}$), it means division. To undo this, you multiply.

Example 3: Solve $3x = 24$

1. Identify the operation: $x$ is being multiplied by $3$.
2. Use the inverse operation: Divide both sides by $3$. $\frac{3x}{3} = \frac{24}{3}$ $x = 8$

Example 4: Solve $\frac{y}{4} = 9$

1. Identify the operation: $y$ is being divided by $4$.
2. Use the inverse operation: Multiply both sides by $4$. $4 \times \frac{y}{4} = 9 \times 4$ $y = 36$

How to Check Your Work

You can always check if your answer is correct by plugging it back into the original equation. For example, in $3x = 24$, if we think $x = 8$, we test it: Does $3 \times 8 = 24$? Yes! The equation is solved correctly.