Question

What is the value of x in the equation 4 and StartFraction 3 Over 10 EndFraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)?

Answer 1

-3

Explanation:

Answer 2

The value of x is –3.

Solution:

Given statement:

4 and Start Fraction 3 Over 10 End Fraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)

Let's convert this into algebraic expression.

`$4(3)/(10) -\left(2(2)/(5)x+5(1)/(2)\right)=(1)/(2)\left(-3(3)/(5)x+1(1)/(5)\right)`

First convert mixed fraction into improper fraction.

`$(43)/(10) -\left((12)/(5)x+(11)/(2)\right)=(1)/(2)\left(-(18)/(5)x+(6)/(5)\right)`

`$(43)/(10) -(12)/(5)x-(11)/(2)=-(18)/(10)x+(6)/(10)`

Now, take LCM and make the denominators same.

LCM of 2, 5, 10 = 10

`$(43)/(10) -(12*2)/(5*2)x-(11*5)/(2*5)=-(18)/(10)x+(6)/(10)`

`$(43)/(10) -(24)/(10)x-(55)/(10)=-(18)/(10)x+(6)/(10)`

Arrange like terms one side of the equation.

`$(18)/(10)x -(24)/(10)x=(6)/(10)-(43)/(10)+(55)/(10)`

`$(18x-24x)/(10) =(6-43+55)/(10)`

`$(-6x)/(10) =(18)/(10)`

`$-6x=(18*10)/(10)`

`$-6x=18`

Divide both sides of the expression by –6, we get

⇒ x = –3

Hence the value of x is –3.