/*! 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 66 \(17-23-14-(-18)\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 66

\(17-23-14-(-18)\)

Short Answer

Expert verified
The answer is -2.

Step by step solution

01

Understand the Expression

The given expression is \(17 - 23 - 14 - (-18)\). This is a sequence of subtraction operations with a negative number, \(-18\), at the end which requires particular attention.
02

Simplify the Negative Parenthesis

Subtracting a negative number is equivalent to adding its positive value. Therefore, \(-(-18)\) becomes \(+18\). The expression now reads: \(17 - 23 - 14 + 18\).
03

Solve the Expression from Left to Right

Begin by solving the expression from left to right. First calculate: \(17 - 23 = -6\).
04

Continue the Calculation

Next, take the result from Step 3 and subtract 14: \(-6 - 14 = -20\).
05

Add the Last Number

Finally, add 18 to the result from Step 4: \(-20 + 18 = -2\).
06

Verify the Calculation

Check each step to ensure the arithmetic operations have been applied correctly. The computations are: \(17 - 23 = -6\), \(-6 - 14 = -20\), \(-20 + 18 = -2\). Each step checks out.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Subtraction
Subtraction is a fundamental arithmetic operation. It involves taking one number (the subtrahend) away from another (the minuend). In the expression \(17 - 23 - 14 - (-18)\), subtraction is used several times.
  • The minuend is the number we start with, like 17 in the first part of the expression.
  • The subtrahend is the number being subtracted, such as 23, 14, or (-18).
To solve the expression, you subtract each number from the result of the previous subtraction. Begin with the first subtraction: \(17 - 23\). This gives \(-6\). Subtraction is commutative, meaning that the order of operations can matter, especially when working with other operations like addition.
Negative Numbers
Negative numbers are essential in math as they represent values below zero. They can often be tricky when combined with subtraction. In our example, consider \(-18\). Although recorded as a subtraction, it turns into an addition due to the double negative.
  • For example, \(-(-18)\) becomes \(+18\), because subtracting a negative is the same as adding the positive counterpart.
When dealing with negative numbers, it's important to carefully review each step to ensure they're accounted for correctly, especially when subtraction results in adding a negative number. Managing negative numbers correctly ensures the accuracy of the math problem.
Order of Operations
The order in which you solve a math problem is crucial. This concept is referred to as the order of operations. For this specific problem, simple left-to-right operations are used, since all math operations are either subtraction or subsequent addition.
  • Start solving from the left: \(17 - 23\) gives \(-6\).
  • Next, take \(-6\) and subtract 14 to get \(-20\).
  • Finally, add 18 to \(-20\) to reach \(-2\).
This sequential solving respects the problem's order of operations, ensuring each calculation is accurately completed step by step. In more complex expressions, operations like multiplication and division would take precedence before addition and subtraction, but in this case, we only handle subtraction and addition.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify each algebraic expression by combining similar terms. $$-6 m-m+17 m$$

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(3 x+5 y+4 x-2 y\) for \(x=-2\) and \(y=3\)

Find the value of \(\frac{h\left(b_{1}+b_{2}\right)}{2}\) for each set of values for the variables \(h, b_{1}\), and \(b_{2}\). (Subscripts are used to indicate that \(b_{1}\) and \(b_{2}\) are different variables.) \(h=17, b_{1}=14\), and \(b_{2}=6\)

Simplify each algebraic expression by combining similar terms. $$5(x-4)+6(x+8)$$

State whether the expressions in each problem are equivalent and explain why or why not. \(9 m+8(3 p-q)\) and \(8(3 p-q)+9 m\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.