/*! 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 14 Solve each equation. $$17=2 t+... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 14

Solve each equation. $$17=2 t+5$$

Short Answer

Expert verified
The solution is \(t = 6\).

Step by step solution

01

Identify the Equation

First, recognize that the equation given is \(17 = 2t + 5\). This is a linear equation with one variable, \(t\). Our goal is to solve for \(t\).
02

Isolate the Variable Term

To solve for \(t\), we need to isolate \(2t\) on one side of the equation. Start by subtracting \(5\) from both sides to get \(12 = 2t\).
03

Solve for the Variable

Now that \(2t = 12\), divide both sides by \(2\) to solve for \(t\). Doing this, we find \(t = 6\).

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.

Solving Linear Equations
Solving equations is like unraveling a mystery where you find the value of the unknown variable. In our exercise, we started with the equation \( 17 = 2t + 5 \). The main task here is to figure out what value of \( t \) makes this equation true. Linear equations such as this one are the simplest type of equations, involving only a first power of the unknown. To solve a linear equation:
  • Understand the goal is to find the value of the variable.
  • Perform operations to maintain the balance between both sides of the equation until the variable is isolated.
This is achieved by following systematic steps such as adding, subtracting, multiplying, or dividing both sides by the same number. Remember, whatever you do to one side of the equation, you must do to the other.
Isolating Variables
The key to solving linear equations efficiently is isolating the variable. This means getting the variable \( t \) by itself on one side of the equation. In the example \( 17 = 2t + 5 \), the term \( 2t \) contains our variable. To isolate it:
  • Look at other terms on the same side (in this case, the \( +5 \) next to \( 2t \)).
  • Perform the opposite operation to get rid of these numbers (since it鈥檚 \( +5 \), subtract \( 5 \) from both sides).
  • Manage each side carefully to keep the equation balanced.
After adjusting, we reached \( 12 = 2t \). The variable is now isolated with a coefficient (2) multiplied by \( t \). Once the term with the variable is alone, use additional steps to solve for the variable itself.
One Variable Equations
Equations with one variable, such as the one we encountered, play a foundational role in algebra. These equations contain only one unknown to solve for, making them particularly straightforward. Here鈥檚 why one-variable equations are important:
  • They introduce basic algebraic concepts and operations.
  • Mastering these builds a foundation for understanding more complex equations.
  • They provide solutions that can often be easily verified by substitution.
In our equation \( 17 = 2t + 5 \), we isolated \( t \) and found it to be \( t = 6 \). Understanding the structure of one-variable equations allows students to develop skills for managing more difficult mathematical problems in the future. Always remember to check your work by plugging the solution back into the original equation to ensure it maintains equality.

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 triangle \(A B C\), the measure of angle \(A\) is \(2^{\circ}\) less than one- fifth of the measure of angle \(C\). The measure of angle \(B\) is \(5^{\circ}\) less than one-half of the measure of angle \(C\). Find the measures of the three angles of the triangle.

Suppose that you are helping a friend with his homework, and he solves the equation \(19=14-x\) like this: $$ \begin{aligned} 19 &=14-x \\ 19+x &=14-x+x \end{aligned} $$ $$ \begin{aligned} 19+x &=14 \\ 19+x-19 &=14-19 \\ x &=-5 \end{aligned} $$ The solution set is \(\\{-5\\}\). Does he have the correct solution set? What would you say to him about his method of solving the equation?

The sum of two numbers is 53 . If three times the smaller number is 1 less than the larger number, find the numbers.

Solve each equation. $$8(n-3)=12$$

Solve each equation. $$-(x+2)+2(x-3)=-2(x-7)$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Pure 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.