Question

Solve and check the solution 5/8 = 1/2(a + 2) please help me

Answer 1

`a=-(3)/(4)`

Explanation:

`(5)/(8)=(1)/(2)\left(a+2\right)\\\\Switch\: sides\\(1)/(2)\left(a+2\right)=(5)/(8)\\\\\mathrm{Multiply\:both\:sides\:by\:}2\\2*(1)/(2)\left(a+2\right)=(5*\:2)/(8)\\\\Simplify\\a+2=(5)/(4)\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\a+2-2=(5)/(4)-2\\\\Simplify\\a=-(3)/(4)`

Check

`(5)/(8) = (1)/(2)\left(-(3)/(4)+2\right) \\\\\mathrm{Multiply\:fractions}:\\\\\quad \:a*(b)/(c)=(a\:* \:b)/(c)\\\\(5)/(8)=(1* \left(-(3)/(4)+2\right))/(2)\\\\(5)/(8)=(1*\left(-(3)/(4)+2\right))/(2)\\(5)/(8)=(-(3)/(4)+2)/(2)\\\\\mathrm{Join}\:-(3)/(4)+2:\quad (5)/(4)\\(5)/(8)=((5)/(4))/(2)\\\\(5)/(8)=(5)/(4*\:2)\\\\(5)/(8)=(5)/(8)`

Answer 2

5/8=1/2(a+2)

distribute

5/8=(1/2)a+1

combine like terms

5/8-8/8=(1/2)a
-3/8=(1/2)a

multiply both sides by 2
-3/4=a
a=-3/4

check

5/8=1/2(-3/4+8/4)
5/8=1/2(5/4)
5/8=5/8