Question

If x = 1/2 what is the value of the following expression?

Answer 1

`=-2x+14`

Explanation:

`\left((1)/(2)\right)^2\cdot \:8-2x+\left(5+7\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=\left((1)/(2)\right)^2\cdot \:8-2x+5+7\\\left((1)/(2)\right)^2\cdot \:8=2\\\left((1)/(2)\right)^2\cdot \:8\\\left((1)/(2)\right)^2=(1)/(2^2)\\\left((1)/(2)\right)^2\\\mathrm{Apply\:exponent\:rule}:\quad \left((a)/(b)\right)^c=(a^c)/(b^c)\\=(1^2)/(2^2)\\\mathrm{Apply\:rule}\:1^a=1\\1^2=1\\=(1)/(2^2)\\=8\cdot (1)/(2^2)`

`\mathrm{Multiply\:fractions}:\quad \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c)\\=(1\cdot \:8)/(2^2)\\\mathrm{Multiply\:the\:numbers:}\:1\cdot \:8=8\\=(8)/(2^2)\\\mathrm{Factor}\:8:\quad 2^3\\\mathrm{Factor\:}8=2^3\\=(2^3)/(2^2)\\\mathrm{Cancel\:}(2^3)/(2^2):\quad 2\\(2^3)/(2^2)\\\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=x^(a-b)\\(2^3)/(2^2)=2^(3-2)\\=2^(3-2)\\\mathrm{Subtract\:the\:numbers:}\:3-2=1\\=2\\=2-2x+5+7\\Group\:like\:terms\\=-2x+2+5+7`

`\mathrm{Add\:the\:numbers:}\:2+5+7=14\\=-2x+14`