Linear Equations

[rex21]

I have tried these problems every way I can think of and cannot get the right answers. I checked my answers in the back of the book so I know my answers aren't right. Could someone help me through them?

x-2 -1 = x-5
5 4

3x -3 = x +2
4 2

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[tkhunny]

Is it this?

\(\displaystyle \frac{x-2}{5} - 1 = \frac{x-5}{4}\)?

If it were me, I'd be tempted to multiply both sides by 20. Why would I do that?

Please show your efforts.

 

[rex21]

Yes that's the correct problem. Not very good putting it on here sorry lol

You would multiply both sides by 20 because it's a common denominator of the two fractions right?

I multipled each side of the equation by the denonimator on that side ex. left side by 5 and right side by 4 which is what I did wrong I'm thinking.

 

[tkhunny]

No worries. Keep trying to write more clearly.

Very good on the Common Denominator

You should get this:

\(\displaystyle 20\left(\frac{x-2}{5} - 1\right) = 20\cdot \frac{x-5}{4}\)

\(\displaystyle 20\cdot\frac{x-2}{5} - 20\cdot 1 = 20\cdot \frac{x-5}{4}\)

\(\displaystyle 4\cdot (x-2) - 20 = 5\cdot (x-5)\)

You need to be VERY clear where this last step came from. I skipped a step on purpose. Fill in the detail I skipped.

 

[rex21]

You mutiplied by 20 but you simplified the numbers to get 4 times (x-2) -20 = 5 times (x-5)

The next step would be 4x-8-20 =5x -25 right?

 

[mmm4444bot]

I multipled each side of the equation by the denonimator on that side

left side by 5 and right side by 4

Oh my gosh! You somehow missed what may be the central concept in solving equations using algebra:

Whatever you do to one side of an equation, you must do to the other side

If you multiply one side of an equation by a different number than you multiply the other side, the two sides will no longer be equal. (Same goes for adding, subtracting, dividing.)


Consider this true equation:

1 = 1

Here is what you did.

(5)(1) = (4)(1)

5 = 4


Here's another example:

x = x

5x = 4x

(This only works when x is zero. Not good.)


Repeat after me: "I will only multiply both sides of an equation by the same number." :cool:

 

[rex21]

The answer that I am getting is x= -3 but my book says the answer is -7 so I'm doing something wrong?

 

[Deleted member 4993]

The answer that I am getting is x= -3 but my book says the answer is -7 so I'm doing something wrong?

If you have posted the correct problem - the correct answer is x = -3

 

[mmm4444bot]

I checked my answers in the back of the book so I know my answers aren't right.

The assumption that a text is correct is usually safe; however, all math texts contain errors, and the answer section is usually where many live.