Solving An Equation With Rational Terms

  • Context: MHB 
  • Thread starter Thread starter Simon T
  • Start date Start date
  • Tags Tags
    Rational Terms
Click For Summary

Discussion Overview

The discussion revolves around solving the equation (2x - 9)/(3x) + 8 = 3/(7x), focusing on the identification of the least common denominator (LCD) and the steps to simplify and solve the equation. The scope includes mathematical reasoning and problem-solving techniques.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the equation and states a proposed solution of x = 0.3956.
  • Another participant clarifies the equation using LaTeX formatting and prompts for the LCD.
  • There is a discussion about determining the LCD, with one participant suggesting it might be 21, while another corrects this to 21x, considering the variable x in the denominators.
  • Participants discuss the process of multiplying through by the LCD and express confusion about the steps involved, particularly regarding the appearance of the number 7 in the simplification.
  • Clarifications are provided on how to handle the multiplication of terms and the cancellation of common factors.
  • Multiple participants express confusion about the steps taken, particularly regarding the derivation of the number 7 in the equation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the steps to solve the equation, with some expressing confusion and seeking clarification on the process. The discussion remains unresolved regarding the correct interpretation and simplification of the equation.

Contextual Notes

There are limitations in the discussion regarding the clarity of the steps taken to solve the equation, particularly in identifying the LCD and the subsequent simplifications. Some assumptions about the manipulation of terms are not explicitly stated.

Simon T
Messages
16
Reaction score
0
Hey guys, I am not to good in Math and I am having issues solving this equation.

2x-9/3x + 8 = 3/7x How do you solve this equation? The answer is supposed to be x = 0.3956?
 
Mathematics news on Phys.org
Re: equation help

Okay, what you mean is:

(2x - 9)/(3x) + 8 = 3/(7x)

or, using $\LaTeX$:

$$\frac{2x-9}{3x}+8=\frac{3}{7x}$$

The first thing we could do is multiply through by the LCD...can you state what the LCD is in this problem?
 
Re: equation help

it doesn't say what the LCD is, we have to figure that out. and yes, the second part of your post is correct
 
Re: equation help

cyrus23 said:
it doesn't say what the LCD is, we have to figure that out. and yes, the second part of your post is correct

Yes, we need to come up with that on our own...can you find it? :D
 
Re: equation help

would it be 21?
 
Re: equation help

cyrus23 said:
would it be 21?

It would be 21 if the denominators were 3 and 7, but there is also $x$ as a factor in both, so the LCD is:

$21x$

So, what do you get when you multiply through by $21x$?
 
Re: equation help

do you multiply both dominators by 21?
 
Re: equation help

cyrus23 said:
do you multiply both dominators by 21?

No, you multiply everything by $21x$:

$$\frac{2x-9}{3x}\cdot21x+8\cdot21x=\frac{3}{7x}\cdot21x$$

After dividing out common factors, we then have:

$$(2x-9)7+8\cdot21x=3\cdot3$$

Now it is a matter of distributing, collecting like terms, and solving for $x$...what do you get?
 
Re: equation help

where did you get 7 + 8 from?
 
  • #10
Re: equation help

cyrus23 said:
where did you get 7 + 8 from?

$$\frac{2x-9}{3x}\cdot21x+8\cdot21x=\frac{3}{7x}\cdot21x$$

$$\frac{2x-9}{3x}(21x)+8\cdot21x=\frac{3}{7x}(21x)$$

$$\frac{2x-9}{\cancel{3x}}(\cancel{3x}\cdot7)+8\cdot21x=\frac{3}{\cancel{7x}}(\cancel{7x}\cdot3)$$

$$(2x-9)(7)+8\cdot21x=3(3)$$

$$7(2x-9)+8\cdot21x=3\cdot3$$
 
  • #11
Re: equation help

where did you get the 7? I am very confused :/
 
  • #12
Re: equation help

cyrus23 said:
where did you get the 7? I am very confused :/

$$\frac{2x-9}{3x}\cdot21x=(2x-9)\frac{21x}{3x}=(2x-9)\frac{3x\cdot7}{3x}=(2x-9)\frac{\cancel{3x}\cdot7}{\cancel{3x}}=(2x-9)7=7(2x-9)$$
 

Similar threads

MHB Absolute Value Equation |3x - 2|/|2x - 3| = 2
  • · Replies 10 ·
Replies
10
Views
2K
MHB Quadratic equations ( solving for zeros/roots) trickey
  • · Replies 1 ·
Replies
1
Views
1K
MHB Which procedure takes the minimum time to solve modulus functions?
  • · Replies 5 ·
Replies
5
Views
1K
MHB [ASK] polynomial f(x) divided by (x - 1)
  • · Replies 2 ·
Replies
2
Views
2K
MHB Solve Equation: $x^4+2x^3-x^2-6x-3=0$
  • · Replies 7 ·
Replies
7
Views
2K
MHB Find Domain & Range of 8 Mathematics Problems for CSE Exam
  • · Replies 1 ·
Replies
1
Views
2K
MHB Equation 2: Prove that ##x^2+2x\sqrt x+3x+2\sqrt x+1=0##
  • · Replies 4 ·
Replies
4
Views
2K
MHB (Seemingly) Random Sequences
  • · Replies 7 ·
Replies
7
Views
2K
High School English Translation of Italian Lecture Notes: Equations & Solutions
  • · Replies 11 ·
Replies
11
Views
2K
MHB Jesusluvsponies's question at Yahoo Answers (Real and rational roots)
  • · Replies 1 ·
Replies
1
Views
1K