Solving Equations

When we solve equations, we are finding the value of the variable that makes the equation true. In other words, we are finding the value that balances both sides of the equation.

Steps for Solving Equations:

1. Isolate the Variable: If the variable is not already isolated on one side of the equation, use inverse operations to move all other terms to the other side.
2. Perform Inverse Operations: Apply inverse operations to both sides of the equation to simplify and solve for the variable.
3. Check Your Answer: After finding the value of the variable, substitute it back into the original equation to ensure that both sides are equal.

Example:

Let's solve the equation 3x + 5 = 17:

Step 1: Isolate the variable.

Subtract 5 from both sides: 3x = 12

Step 2: Perform Inverse Operations.

Divide both sides by 3: x = 4

Step 3: Check Your Answer.

Substitute x = 4 back into the original equation: 3(4) + 5 = 17

12 + 5 = 17

17 = 17 (Both sides are equal, so the solution is correct!)

Study Guide:

Here are some key points to remember when solving equations:

• Use inverse operations to isolate the variable.
• Perform the same operation to both sides of the equation to maintain balance.
• Always check your solution by substituting it back into the original equation.
• Remember that the goal is to find the value of the variable that makes the equation true.

Practice solving equations with different types of operations and remember to always work step by step to ensure accuracy.

Now that you understand the steps and key points for solving equations, you can apply this knowledge to solve various types of equations with confidence!