Question

Evaluate each expression if \(x=-2\) and \(y=3\). \(3 x+y\)

Short answer

-3

Step-by-step solution

- Identify the Given Values

The values provided in the problem are: \(x = -2\) and \(y = 3\).

- Substitute the Given Values

Replace \(x\) and \(y\) in the expression \(3x + y\) with the given values. This gives \(3(-2) + 3\).

- Perform Multiplication

Calculate the product of 3 and \(x = -2\). This gives \(3 \times -2 = -6\).

- Perform Addition

Add the result from the previous step to \(y = 3\). This gives \(-6 + 3\).

- Simplify the Expression

Simplify \(-6 + 3\) to get the final answer, which is \(-3\).

Key concepts

Substitution

Substitution is a fundamental concept in algebra. It involves replacing variables in an expression with given numerical values. Let's see how this works with our example. We have the expression
$$3x + y$$
Given the values:

• x = -2
• y = 3

To substitute these values, we replace x with -2 and y with 3 in the expression. This gives us:
$$3(-2) + 3$$
By substituting correctly, you ensure that you maintain the structure of the original equation, which helps in accurately solving the problem.

Simplification

Simplification is the process of reducing an expression to its most basic form. After substituting the values, we simplify the expression to make it easier to understand or solve. For our example, we substituted the values and got: $$3(-2) + 3$$
Now, perform the multiplication first, as per the order of operations (often remembered as PEMDAS/BODMAS - Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Multiply 3 and -2 to get: $$-6 + 3$$
In the next step, perform the addition to further simplify the expression:
$$-6 + 3 = -3$$
By breaking down the process, simplification becomes easier and lets you focus on solving each part of the expression step-by-step.

Arithmetic Operations

Understanding arithmetic operations is crucial for evaluating algebraic expressions. The main arithmetic operations include:

• Addition (+)
• Subtraction (-)
• Multiplication (×)
• Division (÷)

In our example: $$3(-2) + 3$$ we first perform multiplication and then addition. Let's break it down:

• Multiplication: 3 multiplied by -2, since we have a positive times a negative, the result is -6.
• Addition: Then, add -6 and 3. Adding a positive number to a negative number involves moving up the number line from -6, which gives us -3.

Correctly performing these arithmetic operations ensures accurate evaluation of the expression. Always follow the order of operations to simplify any given algebraic expression.