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
SUMMARY

The discussion focuses on solving the equation (2x - 9)/(3x) + 8 = 3/(7x) using the least common denominator (LCD). Participants determine that the LCD is 21x and demonstrate how to multiply the entire equation by this value to eliminate the denominators. The conversation emphasizes the importance of distributing and collecting like terms to isolate x, ultimately leading to the solution x = 0.3956.

PREREQUISITES
  • Understanding of rational expressions and equations
  • Knowledge of least common denominators (LCD)
  • Ability to perform algebraic operations such as distribution and combining like terms
  • Familiarity with LaTeX for mathematical notation
NEXT STEPS
  • Study how to find the least common denominator in complex fractions
  • Practice solving rational equations with multiple variables
  • Learn about algebraic manipulation techniques, including distribution and factoring
  • Explore the use of LaTeX for formatting mathematical expressions
USEFUL FOR

Students, educators, and anyone looking to improve their skills in solving algebraic equations, particularly those involving rational terms.

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