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# Linear Equation problem... help?

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How do you figure this out?

2m÷5+3=7(4m-3)

Thanks!

Mar 31, 2019

#1
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2m÷5+3=7(4m-3)

$$2m\div 5+3=7(4m-3)\\ \frac{2m}{5}+3=7(4m-3)\\$$

Here is a start.

1) Expand the brackets on the RHS

2) Multiply both sides by 5. that will get rid of the fraction.

3) Subtract 2m from BOTH sides

then see if you can work out how to finish.

Remember that if you do something to one side you MUST do it to the other side as well

The equation must stay balanced. Give that a go and let us know how you get on.

Mar 31, 2019
#2
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So would m=0.8695...?

I did some stuff differently to get that answer because of what I've been taught but I'm probably wrong.

You said to subtract 2m from both sides but wouldn't you be dividing since 2m is multiplication? And when it comes to doing it to both sides which number on each side would you do it to? All of them or just one? So in 2m÷5+3=28m-21 would you multiply 3, 28m and -21 or just 28m or -21?

Thank you again!

Guest Apr 1, 2019
edited by Guest  Apr 1, 2019
#3
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There are different ways of do questions like this.

$$2m\div 5+3=7(4m-3)\\ \frac{2m}{5}+3=7(4m-3)\\$$

Expand the brackets

$$\frac{2m}{5}+3=28m-21\\ \text{Multiply both sides by 5 to get rid of the fraction}\\ 5\left(\frac{2m}{5}+3\right)=5(28m-21)\\ \text{simplify both sides seperately}\\ 5*\frac{2m}{5}+5*3=5*28m-5*21\\ 2m+15=140m-105\\$$

NOW the idea is to get all the lots of letters all on the same side, you have  2m on one sides and 140m on the other side.

I want to get rid off the 2m of the left side SO I have TAKE IT AWAY

but what i do to one side I must do to the other sides as well because the equation must sty balanced!

$$2m+15-2m=140m-105-2m\\ simplify\\ 15=138m-105\\$$

Now I neede to get all the numbers without letters onto the same side.

So I will add 105 to both sides.

$$15+105=138m-105+105\\ simplify\\ 120=138m$$

Only now do I want to seperate the 138 from the m

138m = 138*m

the opposite of times is divide

so   138m divided by 138 = m

also divide is the same a fraction line

so

$$138m\div138 = \frac{138m}{138}=m$$

SO I need to divide both sides by 138

$$\frac{120}{138}=\frac{138m}{138}\\ \frac{120}{138}=m\\ m=\frac{120}{138}\\ m=\frac{20}{23}$$

It is better to keep it as a fraction.

Apr 1, 2019
#4
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Wow you're amazing! Thank you so much for that response. Didn't expect you to go into that much depth. Definitely the best experience I've had on this site by far. Guest Apr 1, 2019
#5
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Thanks, It is important that you study what I have done and fully understand it.

Even if you choose to do it a  different way you should be able to be certain that your (and my) methods are correct and you understand why.

"If you say, 'I don't know if my answer right'    then you do not understand well enough. Melody  Apr 1, 2019