Problem 55 - Prealgebra and Introductory Algebra

Question

Evaluate the expression \(x+y\) for the given values of \(x\) and \(y .\) $$x=-6.175, y=-19.49$$

Step-by-Step Solution

Answer

The result of the expression for the given values of \(x\) and \(y\) is \(-25.665\).

Step 1: Substitute the given values

Insert the given values into the expression. It becomes \((-6.175) + (-19.49)\)

Step 2: Simplify

Sum up the two numbers. The result is \(-6.175 - 19.49 = -25.665\)

Key Concepts

Evaluate Expressions

Evaluating expressions is a fundamental part of prealgebra. This involves taking an expression, which is a combination of numbers, variables, and operations, and calculating its value using known values for the variables.
For example, given the expression \(x + y\), the task was to find its value when \(x = -6.175\) and \(y = -19.49\). Evaluating the expression involves replacing the variables with these values and performing the necessary calculations to find the result.

• First, substitute the values \(x = -6.175\) and \(y = -19.49\) into the expression.
• Next, perform the addition of the two numbers: \((-6.175) + (-19.49)\).
• Finally, simplify the result to get the final answer.

Evaluating expressions is crucial for solving equations and real-world problems as it helps determine the outcome based on given conditions.

Addition of Negative Numbers

Adding negative numbers may seem counterintuitive at first, but it's a straightforward process once you get the hang of it. When you add a negative number, it’s similar to subtracting a positive number.
Consider the expression \((-6.175) + (-19.49)\). Because both numbers are negative, adding them actually involves summing their absolute values and then applying a negative sign to the result.

• Visualize the number line. Both numbers are to the left of zero.
• When you add \(-19.49\) to \(-6.175\), move further left, enhancing the negative effect.
• The result is a larger negative number: \(-25.665\).

Adding negative numbers is essential in understanding how numbers work in different contexts, offering insight into debts, below-zero temperatures, and various practical problems.

Substitution In Algebra

Substitution is a powerful technique used in algebra that allows you to replace variables with specific values to simplify and solve expressions or equations.
For the expression \(x + y\) with \(x = -6.175\) and \(y = -19.49\), substitution involves directly placing these values into the expression. This step-by-step approach makes it easier to handle more complex algebraic problems as well.

• Identify the expression and the values that need to be substituted.
• Replace each variable with its corresponding value.
• Calculate step-by-step, maintaining the order of operations if necessary.

By practicing substitution, students can gain strength in solving equations, unraveling systems of equations, and tackling various mathematical challenges with confidence.