Im a keep editing since this is timed.
#1 x-8a/6=3a-2x
Multiply each term by 6 to remove fraction .
6(x-8a/6)= 3a(6)-2x(6)
X-8a=18a-12x
Add 12x both sides
X+12x-8a=18a-12x+12x
13x-8a= 18a
Add8a both sides
13x-8a+8a=18a+8a
13x=26a
Divide each side by 13
13x/13=26a/13
X= 26a/13
Reduce and cancel common factor .
X= 13(2a)/13(1)
X=2a/1
X=2a
Problem #2
3x-2a=7a find a
Subtract 3x both sides
3x-3x-2a=7a-3x
-2a=7a-3x
Subtract 7a both sides
-2a-7a=7a-7a-3x
5a=-3x
Divide both sides by 5
5a/5=-3x/5
A= -0.6 or -3/5
Problem#3
3(bx-2ab)=b(x-7a)+3ab
Distributed property
3(bx)+3(-2ab)=b(x)+b(-7a)+3ab
Simplify
3bx-6ab=bx-7ab+3ab
Add -7a plus 3ab on right side
3bx-6ab= bx-4ab
Subtract bx both sides
3bx-bx-6ab= bx -bx -4ab
Simplify
2bx-6ab= -4ab
Add 6ab both sides
2bx-6ab+6ab=6ab-4ab
2bx=2ab
Divide 2b both sides
X= 2ab/2b
Cancel 2 common
X= ab/b
X=a
Answer:
For solving an equation for a variable, we need to isolate the variable in the left side of the equation,
1. Given equation,
[tex]\frac{x-8a}{6}=3a-2x[/tex]
[tex]x-8a = 18a - 12x[/tex] ( By cross multiplication ),
[tex]12x+x-8a-18a=0[/tex]
[tex]13x-26a=0[/tex]
[tex]13x = 26a[/tex]
[tex]\implies x = 2a[/tex]
2. [tex]3x-2a=7a[/tex]
[tex]-2a-7a=-3x[/tex]
[tex]-9a=-3x[/tex]
[tex]\implies a = \frac{x}{3}[/tex]
3. [tex]3(bx-2ab)=b(x-7a)+3ab[/tex]
[tex]3bx-6ab = bx - 7ab + 3ab[/tex]
[tex]3bx - bx = 6ab - 7ab + 3ab[/tex]
[tex]2bx=2ab[/tex]
[tex]\implies x = a[/tex]
4. [tex]\frac{2x+3b}{9}=\frac{x-b}{2}[/tex]
[tex]4x+6b = 9x - 9b[/tex]
[tex]4x - 9x = -6b - 9b[/tex]
[tex]-5x=-15b[/tex]
[tex]x=3b[/tex] ( For x )
[tex]b=\frac{x}{3}[/tex] ( For b )
