/*! 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 15 Solve the given equations. $$5... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 15

Solve the given equations. $$5 t+9=-1$$

Short Answer

Expert verified
The solution is \(t = -2\).

Step by step solution

01

Isolate the Variable

To solve the equation \(5t + 9 = -1\), begin by isolating the term with the variable. Subtract 9 from both sides to get: \[5t + 9 - 9 = -1 - 9\] This simplifies to: \[5t = -10\]
02

Divide by the Coefficient

With the equation \(5t = -10\) now isolated, divide both sides by the coefficient of \(t\), which is 5: \[\frac{5t}{5} = \frac{-10}{5}\] This simplifies to: \[t = -2\]

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.

Isolating the Variable
In algebra, "isolating the variable" is one of the most important techniques you will learn. The goal is to get the variable, in our case \(t\), alone on one side of the equation. This makes it easier to understand what the variable equals.

To isolate \(t\), you must perform operations that undo what鈥檚 been done to it. In the equation \(5t + 9 = -1\), \(9\) is being added to \(5t\). So, we need to undo this by doing the opposite operation, which is subtraction in this case. By removing the \(9\), we bring the term with the variable one step closer to being by itself!
Subtracting from Both Sides
Once we know that we need to subtract to isolate the variable, it's time to actually do it. In our equation \(5t + 9 = -1\), we subtract \(9\) from both sides. Why both sides? Because of the golden rule in algebra: whatever you do to one side, you must do to the other.

This keeps the equation balanced, just like a scale. When you subtract \(9\) from both sides, the left side becomes \(5t + 0\), simplifying to \(5t\). The right side becomes \(-10\). So, our equation is now \(5t = -10\).
  • Remove the constant term (known as the numerical part) by subtraction.
  • Ensure both sides of the equation reflect this change.
  • The goal is to focus only on the term with the variable.
Dividing by the Coefficient
With our variable term \(5t\) isolated, the next step is to remove the coefficient (the 5 in front of \(t\)). This is done by division.

The coefficient is what multiplies the variable, and to undo multiplication, we divide. Thus, to solve \(5t = -10\), divide both sides of the equation by \(5\).
  • This results in \(t = \frac{-10}{5}\).
  • By simplifying \(\frac{-10}{5}\), we find \(t = -2\).

Now, \(t\) stands alone, giving us the solution! In summary, dividing by the coefficient is crucial to finally determining the value of the variable.

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

In blending two gasolines of different octanes, in order to find the number \(n\) of gallons of one octane needed, the equation \(0.14 n+0.06(2000-n)=0.09(2000)\) is used. Find \(n,\) given that 0.06 and 0.09 are exact and the first zero of 2000 is significant.

Solve the given problems. Refer to Appendix B for units of measurement and their symbols. The changes in the price of a stock (in dollars) for a given week were \(-0.68,+0.42,+0.06,-0.11,\) and \(+0.02 .\) What was the total change in the stock's price that week?

Assume that all numbers are approximate unless stated otherwise. In 3 successive days, a home solar system produced \(32.4 \mathrm{MJ}\) \(26.704\ \mathrm{MJ},\) and \(36.23\ \mathrm{MJ}\) of energy. What was the total energy produced in these 3 days?

All numbers are approximate. (a) Estimate the result mentally using one- significant-digit approximations of all the numbers, and (b) compute the result using the appropriate rounding rules and compare with the estimate. $$7.84 \times 4.932-11.317$$

Perform the indicated multiplications. The weekly revenue \(R\) (in dollars) of a flash drive manufacturer is given by \(R=x p,\) where \(x\) is the number of flash drives sold each week and \(p\) is the price (in dollars). If the price is given by the demand equation \(p=30-0.01 x,\) express the revenue in terms of \(x\) and simplify.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

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.