Chapter 1: Q34. (page 31)

Solve each equation. Check your solution
$|3 x + 5| = 11$

Short Answer

Expert verified

The solutions of the equations is2 or $\frac{- 16}{3}$

Step by step solution

Step1- Order for solving the equation

To evaluate any equation involving more than one operation, follow the below order operation

First assume the case one in which the equation be a=b.
Secondly assume the case two in which the equation be a=-b.
Solve the equations of both the cases to find the value of algebraic expression
After finding the two values of algebraic expression, put the value in the original equation and check the solution

Step2- Solve the equations

Case1- $a = b$

$\begin{matrix} 3 x + 5 = 11 \\ 3 x = 11 - 5 \\ x = \frac{6}{3} \\ = 2 \end{matrix}$

Case2- $a = - b$

$\begin{matrix} 3 x + 5 = - 11 \\ 3 x = - 11 - 5 \\ x = - \frac{16}{3} \end{matrix}$

Step3- Check the solutions

Put the value of x=2 in the equation $|3 x + 5| = 11$

$\begin{matrix} | 3 x + 5 | = | 3 \times 2 + 5 | \\ = 11 \end{matrix}$

Put the value of $x = \frac{- 16}{3}$ in equation $|3 x + 5| = 11$

$\begin{matrix} | 3 x + 5 | = | 3 \times - \frac{16}{3} + 5 | \\ = | - 11 | \\ = 11 \end{matrix}$

The solution is 2 or $\frac{- 16}{3}$ . Hence, the solution set is $(2, \frac{- 16}{3})$ .

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve each equation. Check your solution
$|3 x + 5| = 11$

Short Answer

Step by step solution

Step1- Order for solving the equation

Step2- Solve the equations

Step3- Check the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Applied Mathematics

Pure Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solution3x+5=11

Short Answer

Step by step solution

Step1- Order for solving the equation

Step2- Solve the equations

Step3- Check the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Applied Mathematics

Pure Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solution
$|3 x + 5| = 11$