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#1 2023-11-20 05:58:28

paulb203
Member
Registered: 2023-02-24
Posts: 128

Rearranging formulae

Make t the subject of the formula

p=(3-2t)/(4+t)

The left hand side was given in the traditional fraction form, with numerator on top of denominator; this is just the same, yeah, with the slash?

Here's my attempt;

Step 1
Mult.both sides by 4+t;
p(4+t)=3-2t
Step 2
Expand brackets;
4p+pt=3-2t
Step 3
Sub.4p from both sides;
pt=3-2t-4p
Step 4
Add 2t to both sides;
pt+2t=3-4p
Step 5
Factorise left side;
t(p+2)=3-4p
Step 6
Divide both sides by (p+2);
t=3-4p/p+2

Last edited by paulb203 (2023-11-20 06:23:28)

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#2 2023-11-20 08:57:39

amnkb
Member
Registered: 2023-09-19
Posts: 194

Re: Rearranging formulae

paulb203 wrote:

Make t the subject of the formula

p=(3-2t)/(4+t)

The left hand side was given in the traditional fraction form, with numerator on top of denominator; this is just the same, yeah, with the slash?

Here's my attempt;

Step 1
Mult.both sides by 4+t;
p(4+t)=3-2t
Step 2
Expand brackets;
4p+pt=3-2t
Step 3
Sub.4p from both sides;
pt=3-2t-4p
Step 4
Add 2t to both sides;
pt+2t=3-4p
Step 5
Factorise left side;
t(p+2)=3-4p
Step 6
Divide both sides by (p+2);
t=3-4p/p+2

grouping symbols are important!
't=3-4p/p+2' means this:

im pretty sure you mean 't = (3-4p)/(p+2)'

the part highlighted in your work is the tricky part
good for you for seeing it!
up

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#3 2023-11-20 09:37:26

KerimF
Member
From: Aleppo-Syria
Registered: 2018-08-10
Posts: 86

Re: Rearranging formulae

amnkb wrote:

Step 1
Mult.both sides by 4+t;
p(4+t)=3-2t

Step 1
Mult.both sides by 4+t, assuming 4+t≠0;
p(4+t)=3-2t

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#4 2023-11-20 10:54:06

amnkb
Member
Registered: 2023-09-19
Posts: 194

Re: Rearranging formulae

KerimF wrote:

Step 1
Mult.both sides by 4+t, assuming 4+t≠0

if 4+t=0 then original rational is undefined
so nonzero 4+t *is* assumed

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#5 2023-11-20 23:26:37

paulb203
Member
Registered: 2023-02-24
Posts: 128

Re: Rearranging formulae

“im pretty sure you meant = (3-4p)/(p+2)'”

Yes. Thanks.

“the part highlighted in your work is the tricky part
good for you for seeing it!”

Thanks. Maths Genie helped, as ever.

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#6 2023-11-21 05:36:08

sologuitar
Member
Registered: 2022-09-19
Posts: 467

Re: Rearranging formulae

paulb203 wrote:

Make t the subject of the formula

p=(3-2t)/(4+t)

The left hand side was given in the traditional fraction form, with numerator on top of denominator; this is just the same, yeah, with the slash?

Here's my attempt;

Step 1
Mult.both sides by 4+t;
p(4+t)=3-2t
Step 2
Expand brackets;
4p+pt=3-2t
Step 3
Sub.4p from both sides;
pt=3-2t-4p
Step 4
Add 2t to both sides;
pt+2t=3-4p
Step 5
Factorise left side;
t(p+2)=3-4p
Step 6
Divide both sides by (p+2);
t=3-4p/p+2

Are you seeking help or teaching a mini lesson?

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#7 2023-11-21 07:59:58

paulb203
Member
Registered: 2023-02-24
Posts: 128

Re: Rearranging formulae

@sologuitar

"Are you seeking help or teaching a mini lesson?"

Ha! Seeking help, always. And just as well, as I screwed up the final part of the answer. Good old amnkb to the rescue though.

This one was puzzling me for days. It was only after watching Maths Genie I realised you could expand brackets, factorise, etc when rearranging the subject.

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#8 2023-11-22 10:47:33

sologuitar
Member
Registered: 2022-09-19
Posts: 467

Re: Rearranging formulae

paulb203 wrote:

@sologuitar

"Are you seeking help or teaching a mini lesson?"

Ha! Seeking help, always. And just as well, as I screwed up the final part of the answer. Good old amnkb to the rescue though.

This one was puzzling me for days. It was only after watching Maths Genie I realised you could expand brackets, factorise, etc when rearranging the subject.

I wonder what amnkb means?

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