How Can I Solve for x of y=cx+dx Using the Textbook Solution?

  • MHB
  • Thread starter Rujaxso
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In summary, to solve for x in the equation y = cx + dx, you need to factor x from the two terms on the right side, then divide both sides by (c+d). This gives the solution x = y/(c+d), with the proviso that (c+d) is not equal to 0.
  • #1
Rujaxso
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\(\displaystyle y = cx + dx\) solve for x textbook solution:\(\displaystyle x = \frac{y}{c+d}\)my steps:

\(\displaystyle \frac{y}{c + d}=\frac{cx + dx}{c + d}\) here I divide to isolate x

\(\displaystyle \frac{y}{c + d}= x + x\) simplifed

\(\displaystyle \frac{y}{c + d}=2x\) adding the two x'sWhat am I missing here?
 
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  • #2
$y = cx+dx$

factor $x$ from the two terms on the right side of the equation ...

$y = x(c+d)$

divide both sides by $(c+d)$ ...

$\dfrac{y}{c+d} = x$
 
  • #3
Thanks Skeeter,

basically reverse distribution of multiplication over addition I guess.
 
  • #4
Rujaxso said:
\(\displaystyle y = cx + dx\) solve for x textbook solution:\(\displaystyle x = \frac{y}{c+d}\)my steps:

\(\displaystyle \frac{y}{c + d}=\frac{cx + dx}{c + d}\) here I divide to isolate x

\(\displaystyle \color{red}{\frac{y}{c + d}=\frac{x(c+d)}{c + d}}\)

\(\displaystyle \color{red}{\frac{y}{c + d}=\frac{x(\cancel{c+d})}{\cancel{c + d}}}\)

see above
 
  • #5
Thanks, got you the first time, I was just trying to confirm the rule/move in English by my 2nd post.
 
  • #6
And if you want to wow your teacher, add the proviso, "for $c+d\not=0$."
 
  • #7
Should I be more impressed by the use of the word proviso? =)

btw you guys and this textbook is the closest thing to a teacher I have right now. Prepare for an onslaught and flurry
of annoying questions in the future.
 

FAQ: How Can I Solve for x of y=cx+dx Using the Textbook Solution?

1. What does "solve for x" mean in this equation?

"Solve for x" means to find the value of the variable x that makes the equation true when substituted into the equation. In other words, we are looking for the solution to the equation where the value of x satisfies the given conditions.

2. What is the purpose of the "y=cx+dx" part of the equation?

The "y=cx+dx" part of the equation is known as the linear function. It represents a relationship between two variables, x and y, where the value of y is dependent on the values of x. The constants c and d determine the slope and intercept of the line, respectively.

3. How do I solve for x in this equation?

To solve for x, we need to isolate the variable on one side of the equation. This can be done by using algebraic operations such as addition, subtraction, multiplication, and division to move the constants and variables to opposite sides of the equation. The resulting value of x will be the solution to the equation.

4. Can this equation have more than one solution for x?

Yes, this equation can have multiple solutions for x. Since the equation represents a line, there can be infinite values of x that satisfy the equation. However, there can also be cases where there is no solution or only one unique solution.

5. Are there any restrictions or limitations to solving for x in this equation?

There may be restrictions or limitations depending on the given values of the constants c and d. For instance, if the value of c is 0, then the equation becomes y = dx, and x can take on any value. However, if c is non-zero, then there may be certain values of x that are not valid solutions. It is important to check for any restrictions or limitations when solving for x in this equation.

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