Question

Solve for x.
6(x - 1) = 9(x + 2)
x = -8
X = -3
X = 3
x = 8

Answer 1

x=-8

Explanation:

6(x-1)= 9(x+2)

6x-6= 9x+18

6x-9x= 18+6

-3x= 24

-3x÷-3= 24÷-3

x=-8

Answer 2

`x=-8`

Explanation:

`6\left(x-1\right)=9\left(x+2\right)\\\mathrm{Expand\:}6\left(x-1\right):\quad 6x-6\\6\left(x-1\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=6,\:b=x,\:c=1\\=6x-6\cdot \:1\\\mathrm{Expand\:}9\left(x+2\right):\quad 9x+18\\9\left(x+2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=9,\:b=x,\:c=2\\=9x+9\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18\\=9x+18\\6x-6=9x+18\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}`

`6x-6+6=9x+18+6\\Simplify\\6x=9x+24\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\6x-9x=9x+24-9x\\Simplify\\-3x=24\\\mathrm{Divide\:both\:sides\:by\:}-3\\(-3x)/(-3)=(24)/(-3)\\Simplify\\(-3x)/(-3)=(24)/(-3)\\\mathrm{Simplify\:}(-3x)/(-3):\quad x\\(-3x)/(-3)\\\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(-b)=(a)/(b)\\=(3x)/(3)\\\mathrm{Divide\:the\:numbers:}\:(3)/(3)=1\\=x\\\mathrm{Simplify\:}(24)/(-3):\quad -8\\(24)/(-3)`

`\mathrm{Apply\:the\:fraction\:rule}:\quad (a)/(-b)=-(a)/(b)\\=-(24)/(3)\\\mathrm{Divide\:the\:numbers:}\:(24)/(3)=8\\=-8\\`