Problem 59 - Prealgebra

Question

Find the value of each of the following expressions when \(a = -2\). $$-4+3 a$$

Step-by-Step Solution

Answer

The value of the expression is -10.

Step 1: Substitute the Value of a

In the given expression \[-4 + 3a\],replace every instance of \(a\) with \(-2\) since we need to find the expression's value when \(a = -2\). This gives us:\[-4 + 3(-2)\].

Step 2: Apply the Multiplication

Now perform the multiplication. Multiply the \(3\) by \(-2\) to get \[3(-2) = -6\]. Now our expression becomes:\[-4 - 6\].

Step 3: Perform Addition

Finally, simplify the expression \[-4 - 6\].Since both numbers are negative, combine them resulting in:\[-4 - 6 = -10\].

Key Concepts

Substitution

In prealgebra, substitution is an essential concept, especially when dealing with expressions and equations. Substitution allows us to insert a specific value in place of a variable. This is particularly useful to evaluate expressions under given conditions. For example, if you have an expression like \[-4 + 3a\], and you're told that \(a = -2\), you replace \(a\) with \(-2\). This gives you a new expression: \[-4 + 3(-2)\].
By substituting variables with their given values, calculations become simpler and you can solve for specific outcomes.
Remember to substitute all instances of the variable to ensure accuracy in your calculations. This process sets the foundation for successfully evaluating and simplifying expressions.

Expression Evaluation

Once you've substituted the variables with their actual values, the next step is to evaluate the expression. Evaluating means simplifying the expression to find its numeric value. After substituting \(-2\) for \(a\) in \[-4 + 3a\], you have \[-4 + 3(-2)\].
This expression involves several arithmetic operations: multiplication and addition (or subtraction, in this case).
Focus on performing these operations in a systematic order, known as the order of operations, to accurately evaluate expressions. Usually, you'll perform multiplication and division first, followed by addition and subtraction.
Evaluating expressions through these steps ensures accuracy in your calculations and aids in developing your problem-solving skills.

Arithmetic Operations

Arithmetic operations such as multiplication, addition, and subtraction are fundamental in evaluating and solving expressions. In the context of our expression, \[-4 + 3(-2)\], begin by multiplying \(3\) by \(-2\), which gives \(-6\).
Thus, the expression simplifies to \[-4 - 6\]. Next, you perform the addition operation, acknowledging that it involves adding negative numbers.
When adding negative numbers like \(-4\) and \(-6\), think of it as "combining" the negatives. This process is similar to addition but keeps the result negative. Hence, \[-4 - 6\] equals \(-10\).
Understanding these arithmetic operations is key to simplifying expressions and solving larger and more complex mathematical problems. You gain a clearer comprehension of how numbers interact using these basic yet powerful operations.