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Chapter 5: Problem 79

Find \(-x\) if \(x=-16\)

Short Answer

Expert verified
-x = 16

Step by step solution

01

Understand the Problem

To find the value of \(-x\) when \(x = -16\), simply substitute the given value of \(x\) into the expression.
02

Substitute the Given Value

Substitute \(x = -16\) into the expression \(-x\). Thus, \(-x = -(-16)\).
03

Simplify the Expression

Simplify \(-(-16)\). The double negative will cancel out, resulting in a positive value. Therefore, \(-(-16) = 16\).

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Key Concepts

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

Understanding Negative Numbers
Negative numbers can sometimes be confusing, but they are simply numbers less than zero. Think of them as positions to the left of zero on a number line.
They are often used to represent things that can be less than zero, like temperature below freezing or debt.
For example, -16 is 16 units to the left of 0 on a number line.
When you see a negative sign in front of a number, it indicates that the number is negative.
Understanding how to work with negative numbers is important in many areas of math and science.
Substitution in Algebra
Substitution means replacing a variable with a number or another expression.
It is a key concept in algebra. For example, if you have an equation or expression and you know the value of a variable, you can substitute that value into the equation.
This helps you find the solution more easily. In the problem provided, you substitute the value of \(x\) with -16 in the expression \(-x\).
So, it becomes \(-(-16)\).
Substitution simplifies expressions and helps solve equations.
Simplification of Expressions
Simplification is the process of making an expression easier to understand and solve.
You can combine like terms, reduce fractions, and simplify roots in this process.
In this problem, the simplification involves eliminating the double negative.
When you have \(-(-16)\), the two negative signs cancel each other out, resulting in 16.
A helpful way to remember this is that a double negative is like turning around twice鈥� you end up facing forward again.
Simplification helps to communicate in the simplest terms and makes calculations easier and faster to perform.

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Most popular questions from this chapter

Perform the indicated operation. $$ \begin{aligned} &\left(2 x^{5 b}+4 x^{4 b}+3 x^{3 b}+8\right)-\\\ &\left(x^{5 b}+2 x^{3 b}+6 x^{2 b}+9 x^{b}+8\right) \end{aligned} $$

Factor completely. $$ x^{6}-2 x^{5}+x^{4}-x^{2}+2 x-1 $$

Factor completely. $$ -10 t^{3}+15 t $$

Solve. A rectangular garden is \(30 \mathrm{ft}\) by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of the old garden. How wide is the walkway?

For \(P(x)\) and \(Q(x)\) as given, find the following. $$ \begin{aligned} &P(x)=13 x^{5}-22 x^{4}-36 x^{3}+40 x^{2}-16 x+75\\\ &Q(x)=42 x^{5}-37 x^{4}+50 x^{3}-28 x^{2}+34 x+100 \end{aligned} $$ $$ 2[Q(x)]-3[P(x)] $$
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