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Chapter 4: Problem 62

Evaluate \(9+t\) if \(t=-1\)

Short Answer

Expert verified
The evaluated expression is 8.

Step by step solution

01

Identify the Expression

The expression we need to evaluate is given as \(9 + t\). We will substitute a value for \(t\) to find the result.
02

Substitute the Given Value of t

Substitute \(t = -1\) into the expression. This changes our expression from \(9 + t\) to \(9 + (-1)\).
03

Simplify the Expression

Calculate the sum by adding \(9\) and \(-1\), which results in \(9 - 1 = 8\).

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Key Concepts

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

Substitution
In algebra, substitution is a valuable technique used to replace variables in an expression with specific values. It's like a plug-and-play strategy that helps you evaluate expressions. In the exercise provided, substitution played a critical role. We replaced the variable \(t\) with the integer value \(-1\). By substituting \(t = -1\) into the original expression \(9 + t\), we were able to transform that expression into something we could readily solve: \(9 + (-1)\). This method is widely used in solving equations and evaluating algebraic expressions because it allows you to simplify a problem by reducing it to numerical calculations.
Simplification
Simplification is the process of making an expression easier to work with by reducing it to its simplest form. After substituting a variable, the next logical step is to simplify the expression. Initially, we had the expression \(9 + (-1)\). Through simplification, we combined the numbers to arrive at a single integer, \(8\). This process might seem straightforward, but it is essential because simplifying an expression makes calculations easier and leads to clearer results.
  • Combine like terms: Look for terms that can be added or subtracted.
  • Eliminate unnecessary parentheses: This helps make the expression neat.
By applying these simplification steps, we reach the final result more directly and without confusion.
Expressions
An expression in mathematics is a combination of numbers, variables, and operations like addition, subtraction, multiplication, and division. It's like a sentence that uses numbers and symbols instead of words. For example, \(9 + t\) is an expression. It consists of:
  • Numerical constant: \(9\)
  • Variable: \(t\) which can vary
  • Operation: '+' indicating addition
Expressions are fundamental components in algebra. They allow us to formulate problems, perform substitutions, and make calculations to find a solution. Understanding how to work with expressions is critical in solving equations and manipulating algebraic forms.
Integers
Integers are a set of numbers that include all whole numbers and their negative counterparts. So, they are like the complete family of whole numbers suspended across a number line:
  • ... -3, -2, -1, 0, 1, 2, 3 ...
In our exercise, both \(9\) and \(-1\) are integers. Working with integers involves understanding how to perform operations like addition and subtraction effectively. The subtraction of integers is handled by thinking of it as an addition of the opposite number. For instance, when calculating \(9 + (-1)\), you essentially add \(9\) and \(-1\) to arrive at \(8\). Understanding integers is crucial in algebra because they form the basis for more complex numbers and operations.

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Most popular questions from this chapter

Evaluate each expression if \(s=-2\) and \(t=3\). $$t^{-4}$$

AlRCRAFT A model of Lindbergh's Spirit of St. Louis has a wingspan of 18 inches. The wingspan of the actual airplane is 46 feet. Write a fraction in simplest form comparing the wingspan of the model and the wingspan of the actual airplane. (Hint: Convert 46 feet to inches.)

Ninety-six centimeters is what part of a meter? $$\mathbf{A} \frac{3}{5}$$ $$B \frac{4}{5}$$ $$\text { C } \frac{23}{25}$$ $$\mathbf{D} \frac{24}{25}$$

Evaluate each expression if \(s=-2\) and \(t=3\). $$s^{t}$$

Numbers can also be expressed in expanded form. Example \(1: 13,548=10,000+3000+500+40+8\) \(=\left(1 \times 10^{4}\right)+\left(3 \times 10^{3}\right)+\left(5 \times 10^{2}\right)+\left(4 \times 10^{1}\right)+\left(8 \times 10^{0}\right)\) Example \(2: 0.568=0.5+0.06+0.008\) $$ =\left(5 \times 10^{-1}\right)+\left(6 \times 10^{-2}\right)+\left(8 \times 10^{-3}\right) $$ Write each number in expanded form. $$5931$$
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