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Chapter 2: Problem 18

Evaluate. \(5 y-1,\) where \(y=-15\)

Short Answer

Expert verified
The expression evaluates to -76.

Step by step solution

01

Substitute the value of y

Start by substituting the given value of \( y = -15 \) into the expression \( 5y - 1 \). This will change the expression to \( 5(-15) - 1 \).
02

Multiply

Now, perform the multiplication in the expression. Multiply 5 by -15 to get \(-75\). So, the expression now becomes \(-75 - 1 \).
03

Simplify

Finally, simplify the expression by subtracting 1 from -75. This results in \(-76\). So, \( 5y - 1 = -76 \) when \( y = -15 \).

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Key Concepts

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

Substitution
Substitution is a fundamental concept in algebra that involves replacing a variable with a specific value. In our exercise, we start by substituting the value of \( y = -15 \) into the expression \( 5y - 1 \). This means that wherever you see \( y \) in the expression, you replace it with \(-15\).
  • Identify the variable in your algebraic expression, which is \( y \) here.
  • Replace \( y \) with its given value, thereby transforming the expression from \( 5y - 1 \) to \( 5(-15) - 1 \).
If executed correctly, this step significantly simplifies the subsequent operations you'll need to perform. The substitution step sets the stage for the evaluation of the expression by transforming it into a manageable arithmetic problem.
Multiplication
After completing the substitution, the next step involves carrying out the multiplication. The expression \( 5(-15) - 1 \) now requires you to multiply \( 5 \) by \(-15\).
  • Understand that multiplying a positive number by a negative number results in a negative product.
  • Perform the multiplication: \( 5 \times (-15) = -75 \).
The expression simplifies to \(-75 - 1\) as a result of this step. Mastering multiplication with positive and negative numbers is crucial, as it can frequently appear in various algebraic problems. Always ensure the signs are handled correctly to avoid mistakes.
Simplification
Simplification completes the evaluation process by reducing the expression to its simplest form. In our problem, the simplified expression is \(-75 - 1\).
  • Subtract \( 1 \) from \(-75\): \(-75 - 1 = -76\).
By simplifying, you arrive at the final evaluated result of the expression for \( y = -15 \). Simplification allows you to work with the simplest form of an expression or equation, making it easier to understand and utilize in further applications. In algebra, simplifying expressions helps in finding solutions more efficiently.

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