Problem 14 Evaluate. $-5 y,$ where \(y=... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 2: Problem 14

Evaluate. $-5 y,$ where $y=-1$

Short Answer

Expert verified

The evaluated result is 5.

Step by step solution

Substitute the Value of y

We are given the expression $-5y$ and need to evaluate it for $y = -1$. The first step is to substitute $-1$ in place of $y$. This gives us $-5(-1)$.

Multiply the Numbers

Now, multiply $-5$ by $-1$. When you multiply two negative numbers, the result is positive. Thus, $-5 \times -1 = 5$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplication of Negatives

When multiplying negative numbers, understanding the rules is key. In algebra, the product of two negative numbers is always positive. This might seem strange at first, but it's a fundamental rule you can rely on.
When you multiply \[-5 \times -1,\]you take two negatives, which "cancel out" to make a positive:

- The rule: Negative 脳 Negative = Positive.
This stems from the pattern of number operations and ensures consistency across math.

If it helps, think about it like this: If owing money (a negative) is undone twice (another negative), you're back in the positive!
Apply this to our example: $-5 \times -1 = 5$.
Remember, the direction flips each time you multiply by a negative.

Variable Substitution

Variable substitution is like replacing a placeholder with its actual value. In algebra, variables are letters used in place of numbers. If you know the value, you can substitute it directly into the expression.
For instance, in $-5y$, when given $y = -1$, replace $y$ with $-1$. This gives:\[-5(-1).\]

This step "substitutes" the variable with a number, making the expression solvable.
Think of it as filling in a blank with the correct missing piece.

Once the substitution is done, you can then perform the operation needed. Whether it's addition, subtraction, or here, multiplication, the key is to replace the variable correctly first.

Mathematical Expressions

Mathematical expressions are combinations of numbers, variables, and operators that represent a value. They might look complex, but they follow simple rules.
The expression $-5y$ consists of:

The coefficient: $-5$, indicating multiplication.
The variable: $y$, which can change value.

To "evaluate" an expression, you calculate its value by performing any operations once all variables have been substituted.
Here鈥檚 how it works:

Substitute known values for variables.
Follow the order of operations, often remembered with PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

This step-by-step approach makes solving expressions logical and straightforward. For our example, inserting $y = -1$ and multiplying gives the result $5$.

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91影视

Evaluate. \(-5 y,\) where \(y=-1\)

Short Answer

Step by step solution

Substitute the Value of y

Multiply the Numbers

Key Concepts

Multiplication of Negatives

Variable Substitution

Mathematical Expressions

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