Question

What is the value of x, when -9(x-5)=x+22 1/2​

Answer 1

x = 2.25

Explanation:

-9(x - 5) = x + 22 1/2

Distribute the nine and then add 9x to both sides

-9x + 45 = x +22 1/2

+ 9x + 9x

Then try to get x alone

45 = 10x + 22 1/2

-22 1/2 -22 1/2

22.5 = 10x

`(22.5)/(10) = (10x)/(10)`

2.25 = x

Answer 2

`\large\boxed{x=(9)/(4)=2(1)/(4)}`

Explanation:

`-9(x-5)=x+22(1)/(2)\qquad\text{multiply both sides by 2}\\\\(2)(-9)(x-5)=2x+(2)\left(22(1)/(2)\right)\\\\-18(x-5)=2x+45\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(-18)(x)+(-18)(-5)=2x+45\\\\-18x+90=2x+45\qquad\text{subtract 90 from both sides}\\\\-18x+90-90=2x+45-90\\\\-18x=2x-45\qquad\text{subtract}\ 2x\ \text{from both sides}\\\\-18x-2x=2x-2x-45\\\\-20x=-45\qquad\text{divide both sides by (-20)}\\\\(-20x)/(-20)=(-45)/(-20)\\\\x=(45:5)/(20:5)\\\\x=(9)/(4)\to x=2(1)/(4)`