Math Is Fun Forum

apple

Member

Registered: 2005-06-03

Posts: 4

Linear Equations

hi i found this really hard because i have exams coming up and we got a practice exam and i have totally forgot this quite of thing

3(x+1) + 5x+3/2 = -2

Can any body help me??????????

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Linear Equations

Easy (I think) 

This kind of problem just needs playing with until it neatens up.

Lets have a go:

Start with: 3(x+1) + 5x+3/2 = -2

Expand the brackets: 3x+3 + 5x+3/2 = -2

Combine the x's: 3x+5x + 3 +3/2 = -2
then add: 8x + 3 +3/2 = -2

Now add 3 and 3/2: 8x + 9/2 = -2

Now subtract 9/2 from both sides: 8x + 9/2 -9/2 = -2 -9/2
Simplify: 8x = -2 -9/2

Combine -2 and -9/2: 8x = -13/2

Divide both sides by 8:  8x/8 = (-13/2)/8

Simplify: x = -13/16 DONE

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

apple

Member

Registered: 2005-06-03

Posts: 4

Re: Linear Equations

thanks but i wrote it wrong ....

its actually 3(x+1) + (5x+3)/2 = -2

..... so 5x+3 is all divided by two

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Linear Equations

LOL ... OK start again (I will work it out and post in a few minutes)

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Linear Equations

Start: 3(x+1) + (5x+3)/2 = -2

Expand brackets: 3x+3 + (5/2)x + 3/2 = -2

Multiply both sides by 2 (makes it easier not to have the fractions): 6x+6 + 5x + 3 = -4

Combine the x's: 11x+6 + 3 = -4

Combine 6 and 3: 11x+9 = -4

Subtract 9 from both sides: 11x+9-9 = -4-9
Simplify: 11x = -13

Divide both sides by 11: 11x/11 = -13/11

Simplify: x = -13/11

Now, let me check ...

3(-13/11 +1) + (5 * (-13/11)+3)/2 = -2
3(-2/11) + (-65/11 + 33/11)/2 = -2
-6/11 + (-32/11)/2 = -2
-6/11 - 16/11 = -2
-22/11 = -2
-2 = -2

YAY!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

apple

Member

Registered: 2005-06-03

Posts: 4

Re: Linear Equations

thats what i came up with when i did it ... but i thought it might be wrong.

apple

Member

Registered: 2005-06-03

Posts: 4

Re: Linear Equations

o wow thank u so much! now i understand!

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Linear Equations

Well, we might both be wrong ....

Nah!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman