Problem 60 - Prealgebra

Question

Find the value of each of the following expressions when \(a = -2\). $$-6+5 a$$

Step-by-Step Solution

Answer

The result of the expression is -16.

Step 1: Identify the expression

The expression given is \[-6 + 5a\] where we need to substitute the value of \(a = -2\).

Step 2: Substitute the given value

Substitute \(a = -2\) into the expression:\[-6 + 5(-2)\]

Step 3: Multiply coefficients

Calculate the multiplication part:\[5(-2) = -10\]

Step 4: Perform addition

Now, substitute and calculate the result:\[-6 + (-10) = -6 - 10\]

Step 5: Simplify the expression

Finally, simplify the result:\[-6 - 10 = -16\]

Key Concepts

Substitution Method

The substitution method is a process used to evaluate an algebraic expression by replacing the variables with their given numerical values. This method is an essential skill in prealgebra, allowing students to find the value of expressions under certain conditions. To apply the substitution method effectively, follow these steps:

• Identify the variable in the expression. In our example, the variable is \( a \).
• Find the value assigned to the variable, which is \( a = -2 \) in this case.
• Replace all occurrences of the variable in the expression with its given value. This transforms
  our expression \( -6 + 5a \) into \( -6 + 5(-2) \).

This substitution turns an algebraic expression into a numerical one, making it much easier to solve.

Negative Numbers

Handling negative numbers can be tricky, but understanding them is crucial for solving expressions accurately. Negative numbers are simply numbers less than zero. They are typically represented with a minus sign (-) in front. In mathematics, especially in prealgebra, negative numbers can change the direction

• Addition with a negative number means moving towards more negative (or less positive) values. For example, \(-6 + (-10)\) means we combine together two negatives, moving further away from zero.
• Multiplying by a negative flips the sign of the number. For instance, \(5(-2)\) results in \(-10\), as a positive times a negative yields a negative.

Always pay attention to the signs. Remembering these rules will help you avoid common pitfalls when working with negative numbers.

Simplifying Expressions

Simplifying expressions involves combining like terms and reducing the expression to its simplest form. After substituting values and performing operations, your goal should be to simplify the expression as much as possible.When simplifying expressions involving both positive and negative numbers:

• Perform arithmetic operations step-by-step. For instance, in the solution \(-6 + (-10)\), recognize that adding a negative is the same as subtracting the positive counterpart
• Always combine like terms, which are terms with the same variable or constant, whether positive or negative. Our original expression was transformed and simplified to \(-16\)

This method not only gives you the final answer but also ensures you truly understand the underlying mathematical processes.