Problem 52 - Prealgebra

Question

Evaluate each expression. $$2 t+8, t=-3$$

Step-by-Step Solution

Answer

The value of the expression is 2.

Step 1: Substitute the value of t

Start by substituting the given value of \(t = -3\) into the expression \(2t + 8\).

Step 2: Perform the multiplication

Multiply the coefficient \(2\) by the substituted value \(-3\). So, calculate \(2 imes (-3)\), which equals \(-6\).

Step 3: Add the constant

Now add the constant \(8\) to the result of the multiplication. So, calculate \(-6 + 8\), which equals \(2\).

Key Concepts

Substitution in Algebra

Substitution is like replacing variables with numbers to make solving expressions easier. In prealgebra, when given a specific value for a variable, you simply plug that value into the expression wherever the variable appears. This is known as substitution.

For example, if you're given the expression \(2t + 8\) and the value \(t = -3\), you substitute \(-3\) for \(t\). Hence, the expression becomes \(2(-3) + 8\).

Substitution makes algebraic expressions concrete by removing the letter and replacing it with a number, which you can then calculate further. It's a crucial skill in mathematics because it helps you evaluate and simplify expressions and equations.

Understanding Multiplication in Algebra

In algebra, multiplication usually involves using coefficients and variables. A coefficient is a number that multiplies a variable; in \(2t\), 2 is the coefficient, and it multiplies \(t\).

When you substitute a value into an expression, as with \(t = -3\), you then perform multiplication with that number: Multiply 2 by \(-3\) to get \(-6\). This step is crucial because it translates an abstract expression into a numerical value, which is easier to handle and further calculate.

Always remember, multiplication follows the rules of arithmetic operation where it distributes across addition or subtraction if needed. But in this example, simply perform the multiplication first after substituting before proceeding to any additional operations.

Addition in Algebra

Addition in algebra often involves combining the results of substitution and multiplication with constants in the expression. Once you've performed any necessary multiplication, as we did with finding that \(2(-3) = -6\), the next step is addition.

Here, you add the constant from the expression, which is 8, to the product obtained: \(-6 + 8\).

This addition gives you the final simplified value of the expression, which is 2. Addition helps combine different parts of an expression after other operations have been carried out, creating a single, simplified result. It's an important final step in evaluating algebraic expressions effectively.