# help with linear equations (chapter review questions)

• Jul 2nd 2008, 06:06 AM
fresh_
help with linear equations (chapter review questions)
hey need help

1)3-2x/5-x-7/6

working out
6(3-2x)-5(x-7) ≤ -2(30)
-17x ≤ -113
x -113/-17 ?? wrong

2)a/x+a + b/x-b = a+b/x+c, for x
first i multiply everything on the denominator to get the same denominator therefore mulitpying the top
so, (ax-b)(x+c) + (bx+ba)(x+c) = (ax^2+a^2+bx+ba)(x-b)
expanded it and then collected like terms.
so, axc - bx+bxc+acb-a^2x+b^2 x = -a^2 b -b^2a-bac+bc
then where to ?

3)the formula for converting degrees Celsius,C, to degrees Farenheit,F, is F=9/5C+32
a)If xC=xF, find x.
b)If kF=(-3k)C, find k

thanks for anyone who can help(Rofl)
• Jul 2nd 2008, 07:16 AM
Isomorphism
Quote:

Originally Posted by fresh_
2)a/x+a + b/x-b = a+b/x+c, for x
first i multiply everything on the denominator to get the same denominator therefore mulitpying the top
so, (ax-b)(x+c) + (bx+ba)(x+c) = (ax^2+a^2+bx+ba)(x-b)
expanded it and then collected like terms.
so, axc - bx+bxc+acb-a^2x+b^2 x = -a^2 b -b^2a-bac+bc
then where to ?

$\frac{a}{x+a} + \frac{b}{x-b} = \frac{a+b}{x+c}$

$a(x-b)(x+c)+ b(x+a)(x+c) = (a+b)(x-b)(x+a)$

$a(x^2 + (c-b)x - bc)+ b(x^2 + (c+a)x + ac) = (a+b)(x^2+(a-b)x - ab)$

$(a+b) x^2 + (ac-ab+bc+ba)x - abc+abc = (a+b)x^2+(a^2-b^2)x - ab(a+b)$

$(ac+bc)x = (a^2-b^2)x - ab(a+b)$

$(a^2-b^2 - ac -bc)x = ab(a+b)$

$(a+b)(a-b-c)x = ab(a+b)$

if $a+b \neq 0$, then:

$x = \frac{ab}{a-b-c}$
• Jul 2nd 2008, 10:28 AM
masters
Quote:

Originally Posted by fresh_
hey need help

1)3-2x/5-x-7/6

working out
6(3-2x)-5(x-7) ≤ -2(30)
-17x ≤ -113
x -113/-17 ?? wrong

thanks for anyone who can help(Rofl)

Something is obviously missing here!!(Wondering)
• Jul 2nd 2008, 10:36 AM
topsquark
Quote:

Originally Posted by fresh_
1)3-2x/5-x-7/6

working out
6(3-2x)-5(x-7) ≤ -2(30)
-17x ≤ -113
x -113/-17 ?? wrong

What?? The first line is not an inequality, so I don't know how the second line comes about, and then it disappears in the last line. Fix this up and we can help you.

-Dan
• Jul 2nd 2008, 10:39 AM
topsquark
Quote:

Originally Posted by fresh_
3)the formula for converting degrees Celsius,C, to degrees Farenheit,F, is F=9/5C+32
a)If xC=xF, find x.
b)If kF=(-3k)C, find k

$F = \frac{9}{5}C + 32$

For the first one we have
$x = \frac{9}{5}x + 32$

$x - 32 = \frac{9}{5}x$

$5(x - 32) = 9x$

$5x - 180 = 9x$

etc.

For the second one use
$k = \frac{9}{5}(-3k) + 32$
and solve for k in a similar manner.

-Dan
• Jul 2nd 2008, 08:23 PM
fresh_
1)3-2x/5 - x-7/6 ≤ 2

working out
6(3-2x)-5(x-7) ≤ -2(30)
18-12x - 5x+35 ≤ -60
-17x ≤ -113
x -113/-17 ?? wrong

• Jul 2nd 2008, 10:52 PM
Isomorphism
Quote:

Originally Posted by fresh_
1)3-2x/5 - x-7/6 ≤ 2

working out
6(3-2x)-5(x-7) ≤ -2(30)
18-12x - 5x+35 ≤ -60
-17x ≤ -113
x -113/-17 ?? wrong

$\frac{3-2x}5 - \frac{x-7}6 \leq 2$

Multiply by 30 throughout and since 30 is poitive, inequality does not change.

$6(3-2x) - 5(x-7) \leq 60$

$18 -12x - 5x+ 35 \leq 60$

$-17x + 53 \leq 60$

Add 17x on both sides and subtract 60 on both sides,

$-7 \leq 17x \Rightarrow 17x \geq -7 \Rightarrow x \geq -\frac7{17}$