Question

X = 4/5 (x+10)
Find x

Answer 1

40

Explanation:

x+10= x 5/4

x +10= 5x/4

4x+40= 5x

40= x

x=40

Answer 2

`x=40`

Explanation:

`x=(4)/(5)\left(x+10\right)\\\mathrm{Expand\:}(4)/(5)\left(x+10\right):\quad (4)/(5)x+8\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=(4)/(5),\:b=x,\:c=10\\=(4)/(5)x+(4)/(5)\cdot \:10\\=(4)/(5)x+10\cdot (4)/(5)\\10\cdot (4)/(5)=8\\10\cdot (4)/(5)\\\mathrm{Multiply\:fractions}:\quad \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c)\\=(4\cdot \:10)/(5)\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:10=40\\=(40)/(5)`

`\mathrm{Divide\:the\:numbers:}\:(40)/(5)=8\\=(4)/(5)x+8\\x=(4)/(5)x+8\\\mathrm{Subtract\:}(4)/(5)x\mathrm{\:from\:both\:sides}\\x-(4)/(5)x=(4)/(5)x+8-(4)/(5)x\\Simplify\\x-(4)/(5)x=(4)/(5)x+8-(4)/(5)x\\\mathrm{Simplify\:}x-(4)/(5)x:\quad (1)/(5)x\\x-(4)/(5)x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(1-(4)/(5)\right)\\1-(4)/(5)=(1)/(5)\\=(1)/(5)x\\1-(4)/(5)`

`\mathrm{Convert\:element\:to\:fraction}:\quad \:1=(1\cdot \:5)/(5)\\=(1\cdot \:5)/(5)-(4)/(5)\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad (a)/(c)\pm (b)/(c)=(a\pm \:b)/(c)\\=(1\cdot \:5-4)/(5)\\1\cdot \:5-4=1\\1\cdot \:5-4\\\mathrm{Multiply\:the\:numbers:}\:1\cdot \:5=5\\=5-4\\\mathrm{Subtract\:the\:numbers:}\:5-4=1\\=1\\=(1)/(5)\\=(1)/(5)x\\\mathrm{Simplify\:}(4)/(5)x+8-(4)/(5)x:\quad 8\\(4)/(5)x+8-(4)/(5)x`

`\mathrm{Add\:similar\:elements:}\:(4)/(5)x-(4)/(5)x=0\\=8\\(1)/(5)x=8\\\mathrm{Multiply\:both\:sides\:by\:}5\\5\cdot (1)/(5)x=8\cdot \:5\\\mathrm{Simplify}\\x=40`