/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 41 Evaluate the expression. $$ ... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 41

Evaluate the expression. $$ |-29|+7 $$

Short Answer

Expert verified
The result of the expression is 36.

Step by step solution

01

Understanding the Absolute Value

The absolute value of a number is its distance from zero on the number line. Negative numbers become positive, positive numbers stay as they are, and zero remains zero. Here we have the number \(-29\), so its absolute value will be \(29\).
02

Perform Addition

After finding the absolute value, add 7 to the obtained value. Calculation is as follows: \(29 + 7 = 36\).

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Key Concepts

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

Evaluating Expressions
When we talk about evaluating expressions, imagine it as following a recipe. Each ingredient is like a component of the expression, and the mathematical operations are the steps. For instance, in the expression \( |-29|+7 \) our key ingredients are the absolute value of -29 and the number 7. Evaluating begins by working out the absolute value and then 'adding in' the 7, just like you might mix ingredients together to make a cake.

Evaluation is crucial for simplifying mathematical sentences into single numerical values that you can understand and use. Always follow the order of operations, which, although not directly applicable here, is generally good practice in more complicated expressions.
Absolute Value of a Number
Think of the absolute value as a 'no negativity allowed' rule for numbers. It's the distance a number is from zero on the number line, without any direction. Since distance can't be negative, neither can the absolute value. If you're at point -29 on the number line, to find out how far you are from zero, you simply disregard the minus sign, leaving you with 29, the absolute value of -29.

Absolute value is often represented by vertical bars, like this: \( |-29| = 29 \) It can be helpful for understanding real-life scenarios where only magnitude is important, like the strength of an earthquake.
Number Line
The number line is a straight, horizontal line marked with numbers at equal intervals. On this line, you'll find positive numbers stretching out to the right from zero and negative numbers extending to the left. For visual learners, the number line is invaluable because it turns abstract concepts into something you can physically see and touch.

To find the absolute value on the number line, you measure how many steps it takes to get back to zero. No matter which direction you're coming from, left or right, the number of steps is the absolute value. For \( |-29| \) on the number line, you start at -29 and move 29 'steps' to the right to return to zero.
Performing Addition
Performing addition is as straightforward as it gets: you simply combine numbers together to find their total. After you've calculated the absolute value in the expression \( |-29| \) and gotten your 29, you then add the next number in line. In our initial exercise, that's 7. So you calculate \( 29 + 7 = 36 \) and voil脿, the total is 36.

The beauty of addition is in its simplicity鈥攚hether you're adding positive or negative numbers, you're working towards a sum. It's just like gathering a pile of apples; add one more, and you have one more apple鈥攊t's that easy.

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Most popular questions from this chapter

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ -y\left(-y^{2}+y\right) $$

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ 15 x+(-4 x) $$

Use the distributive property and mental math to simplify the expression. $$ \begin{aligned} 9(1.95) &=9(?-2) \\ &=? \end{aligned}$$

LOGICAL REASONING Decide whether the statement is true or false If false, rewrite the right-hand side of the equation so the statement is true. $$ -3.5(6.1+8.2) \stackrel{2}{=}-3.5(6.1)-3.5(8.2) $$

LOGICAL REASONING Decide whether the statement is true or false If false, rewrite the right-hand side of the equation so the statement is true. $$ \frac{2}{9}\left(\frac{1}{3}-\frac{4}{9}\right) \stackrel{?}{=} \frac{2}{9}\left(\frac{1}{3}\right)-\frac{2}{9}\left(\frac{4}{9}\right) $$
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