Solving Equations (Linear)

[Probability]

I am trying to learn how to solve linear equations and simplify, where in this example 3a is not equal to -2b.

This is what I have done so far, I am also to understand that where terms are not the same then they cannot be simplified.

3a(3a – x) = 2b(x + 2b)​

​

Solution

Multiply out the brackets;

9a² – 3ax = 2bx + 4b²​

9a² – 4b² = 3ax – 2bx ​

9a² – 4b² = (3a – 2b)x

​

Have I got this right or am I missing something?

Thanks

Probability

 

[wjm11]

I am trying to learn how to solve linear equations and simplify, where in this example 3a is not equal to -2b.

This is what I have done so far, I am also to understand that where terms are not the same then they cannot be simplified.

3a(3a – x) = 2b(x + 2b)​

Solution

Multiply out the brackets;

9a² – 3ax = 2bx + 4b²
9a² – 4b² = 3ax – 2bx
9a² – 4b² = (3a – 2b)x

​

Have I got this right or am I missing something?

Thanks

Probability

I suspect you have not stated your problem fully. Are you supposed to solve for x? If so, that means you must get x on one side by itself and simplify the other side as much as possible.
You are off to a good start, but you have a few more steps to complete. Factor the left hand side (hint: difference of two squares), then divide both sides by (3a - 2b). Finally, cancel if possible.

 

[Probability]

I suspect you have not stated your problem fully. Are you supposed to solve for x? If so, that means you must get x on one side by itself and simplify the other side as much as possible.
You are off to a good start, but you have a few more steps to complete. Factor the left hand side (hint: difference of two squares), then divide both sides by (3a - 2b). Finally, cancel if possible.

Thanks, this is what I have done since posting originally.

x = 9a2 - 4b2
3a - 2b

x = (3a - 2b)(3a + 2b)
3a - 2b

x = 3a + 2b

I am not sure?

 

[wjm11]

Thanks, this is what I have done since posting originally.

x = 9a2 - 4b2
3a - 2b

x = (3a - 2b)(3a + 2b)
3a - 2b

x = 3a + 2b

I am not sure?

Looks good.

 

[mmm4444bot]

x = (3a - 2b)(3a + 2b)
3a - 2b

Instead of trying to draw factions when typing math, use the forward slash / to show division:

x = (3a - 2b)(3a + 2b)/(3a - 2b)

I am not sure [if my answer is correct]

You may check your answer by substituting your result for x into the original equation and simplifying. If you end up with a true statement, that confirms your answer. :cool:

 

[JeffM]

Thanks, this is what I have done since posting originally.

x = 9a2 - 4b2
3a - 2b

x = (3a - 2b)(3a + 2b)
3a - 2b

x = 3a + 2b

I am not sure?

Show exponentiation as a^2. Show division by (9a^2 - 4b^2) / (3a - 2b).

The way to be sure is to put your solution back into the original equation to see if it results in a correct equation.

\(\displaystyle 3a(3a - x) = 3a\{3a - (3a + 2b)\} = 3a(3a - 3a - 2b) = 3a * (- 2b) = - 6ab.\)

\(\displaystyle 2b(x + 2b) = 2b\{(3a + 2b) + 2b\} = 2b(3a + 2b + 2b) = 2b(3a + 4b) = 6ab + 8b^2 \ne - 6ab.\)

Your answer is wrong. Let's figure out why.

\(\displaystyle 3a(3a - x) = 2b(x + 2b) \implies 9a^2 - 3ax = 2bx + 4b^2 \implies 9a^2 - 4b^2 = 3ax + 2bx = x(3a + 2b) \implies\)

\(\displaystyle x = \dfrac{9a^2 - 4b^2}{3a + 2b} = \dfrac{(3a + 2b)(3a - 2b)}{3a + 2b} = 3a - 2b.\)

Let's check.

\(\displaystyle 3a(3a - x) = 3a\{3a - (3a - 2b)\} = 3a(3a - 3a + 2b) = 3a * 2b = 6ab.\)

\(\displaystyle 2b(x + 2b) = 2b\{(3a - 2b) + 2b\} = 2b(3a - 2b + 2b) = 2b *3a = 6ab.\)

This answer is correct. It is important to check your work. You will make fewer mistakes that way. (Sadly, we all make mistakes.)

 

[Probability]

Instead of trying to draw factions when typing math, use the forward slash / to show division:

x = (3a - 2b)(3a + 2b)/(3a - 2b)





You may check your answer by substituting your result for x into the original equation and simplifying. If you end up with a true statement, that confirms your answer. :cool:

Thanks for your replies, yes I will use the forward slash for division and yes I will check the answer by substitution.

Regards

Probability