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.

**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.**Perform Inverse Operations:**Apply inverse operations to both sides of the equation to simplify and solve for the variable.**Check Your Answer:**After finding the value of the variable, substitute it back into the original equation to ensure that both sides are equal.

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.

**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!)

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!

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Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to solve problems in other areas of mathematics, such as number and measurement.