Solving Equations: 5x/4 + 1/2= x - 1/2

Question

shane_b · Answer

Do you know where to start?

anonymous · Answer

I know I have to get rid of the 1/2 on the left, right?

shane_b · Answer

If you want to start there, that's fine.  What does that leave you with?

anonymous · Answer

5x/4=2(x- 1/2)?

shane_b · Answer

Close but no :)

Subtract 1/2 from both sides to get:$$\frac{5x}{4}=x-\frac{1}{2}-\frac{1}{2}=x-1$$

shane_b · Answer

Do you see why the above is correct?

anonymous · Answer

yes, your subtracting 1/2 from both sides, not flipping the fraction and multiplying both sides like I did

shane_b · Answer

Ok...so now you have:$$\frac{5x}{4}=x-1$$Now what?

shane_b · Answer

I think you have it from here...let's see :)

anonymous · Answer

multiply both sides by 4 leaving me with 
5x=-4
then divide by five?
x=-4/5

shane_b · Answer

Check your answer...there's a mistake there

shane_b · Answer

(in the first line)

anonymous · Answer

lol divide by five... my bad

shane_b · Answer

I think you took the wrong off ramp :)

$$\frac{5x}{4}=x-1$$$$5x=4(x-1)$$$$5x=4x-4$$$$x=-4$$

anonymous · Answer

ooooh, thank you so much I've been struggling with this problem since this morning

shane_b · Answer

No worries...it takes practice

lgbasallote · Answer

here comes another method...

$$\frac{5x}{4} + \frac 12 = x - \frac 12$$
multiply everything by the LCM..in this case 4 (so the denominator thingies will get cancelled)
$$5x + 2 = 4x - 2$$
subtract 4x from both sides
$$x + 2 = -2$$
subtract 2 from both sides
$$x = -4$$
although...this method takes more practice...