To evaluate algebraic expressions for specific values of variables, follow these easy steps:

Step 1: Identify the Expression

First, find the algebraic expression you need to solve.

An algebraic expression usually has numbers, letters (which we call variables), and math operations (like adding, subtracting, multiplying, and dividing).

For example, look at this expression:

$$3x^2 + 5y - 7$$

Step 2: Substitute Variable Values

Next, put the specific values for the variables into the expression.

Let’s say we have $x = 2$ and $y = 3$.

You would replace $x$ and $y$ in the expression like this:

$$3(2)^2 + 5(3) - 7$$

Step 3: Perform the Operations

Now, you need to do the math in the correct order. This is where we use PEMDAS, which stands for:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

1. Calculate Exponents: Start with the part $3(2)^2$. Look at $2^2$ first:

   $$2^2 = 4$$

   Now put that back into the expression:

   $$3(4) + 5(3) - 7$$

2. Perform Multiplication: Next, multiply the numbers:

   $$3 \cdot 4 = 12 \quad \text{and} \quad 5 \cdot 3 = 15$$

   Now the expression looks like this:

   $$12 + 15 - 7$$

3. Perform Addition and Subtraction: Finally, we do the addition and subtraction from left to right.

   Start with this addition:

   $$12 + 15 = 27$$

   Now subtract $7$:

   $$27 - 7 = 20$$

Step 4: State the Result

After doing all the math, say the result clearly.

So, when you evaluate the expression $3x^2 + 5y - 7$ with $x = 2$ and $y = 3$, you get:

$$20$$

Summary

To sum it up, you can evaluate algebraic expressions by:

1. Finding the algebraic expression.
2. Putting the values in for the variables.
3. Following the order of operations to do the math.
4. Clearly stating the final answer.

Important Note

Knowing how to evaluate algebraic expressions is an important skill in math. It helps in many areas, like science, engineering, and data analysis.

For example, about 74% of high school students said they use algebraic expressions to solve real-life problems. This shows how useful and relevant these math skills are in everyday life.

By learning these steps, students can get better at solving problems and get ready for even more complicated math later on.