/*! 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 102 Solve for x. $$5-2 x \geq 17$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 102

Solve for x. $$5-2 x \geq 17$$

Short Answer

Expert verified
x 鈮� -6

Step by step solution

01

Isolate the variable term

To isolate the term involving x, we need to move the constant on the left side to the right side of the inequality. Subtract 5 from both sides:\[ 5 - 2x - 5 \geq 17 - 5 \]This simplifies to:\[ -2x \geq 12 \]
02

Solve for x

Divide both sides of the inequality by -2. Remember to reverse the inequality sign when dividing both sides by a negative number:\[ \frac{-2x}{-2} \leq \frac{12}{-2} \]This simplifies to:\[ x \leq -6 \]

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.

Isolation of Variable
When solving inequalities, one of the key steps is isolating the variable. This simply means we want the variable (in this case, x) on one side of the inequality by itself.

For example, in the inequality: \[ 5 - 2x \geq 17 \]

The term with x is \-2x\. To isolate it, we start by moving the constant term (which is 5) from the left side to the right side of the inequality.

We do this by subtracting 5 from both sides:
\[ 5 - 2x - 5 \geq 17 - 5 \]

This simplifies to: \[ -2x \geq 12 \]

Isolating the variable helps us focus on the term containing x, making it easier to solve the inequality.
Inequality Reversal
When working with inequalities, it's crucial to remember a key rule: whenever we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality sign.

Let's consider the previous result: \[ -2x \geq 12 \]

To solve for x, we need to divide both sides by -2. However, dividing by a negative number reverses the inequality:
\[ \frac{-2x}{-2} \leq \frac{12}{-2} \]

Here, the \geq\ sign changes to a \leq\ sign, resulting in: \[ x \leq -6 \]

Failing to reverse the sign can lead to incorrect solutions, so always remember this important step.
Dividing by Negative Numbers
Dividing by negative numbers in inequalities is a special aspect that requires extra attention.

In the final step of our example: \[ -2x \geq 12 \]

We divided both sides by -2: \[ \frac{-2x}{-2} \leq \frac{12}{-2} \]

The division changes the inequality sign from \geq\ to \leq\. This reversal occurs because negative numbers flip the order of the inequality when multiplied or divided.

As a general rule, whenever we multiply or divide both sides of an inequality by a negative number, we must flip the inequality sign.
By keeping this rule in mind, we ensure our solutions are correct and accurately reflect the relationship between the variables.

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

Convert each number into standard notation. $$2.8 \times 10^{4}$$

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(3 x+7)(5 x+4)$$

Do your computation using scientific notation. $$(0.004)(250)$$

Suppose that the price \(p\) of a given item is related to the number of items sold \(x\) by the equation \(p=50-0.004 x\). The revenue \(R\) is computed by multiplying the price per item \(p\) by the number of items \(x\). Thus, \(R=x(50-0.004 x)\). Find the increase in revenue if \(x\) is increased by 500 .

A car rental agency charges \(\$ 15\) per day plus \(\$ 0.20\) per mile. If a 3 -day rental cost \(\$ 72,\) how many miles were driven?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Decision Maths

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.