Question

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

Answer 1

Answer:

x = 2.25

Step-by-step 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

   $\frac{22.5}{10} = \frac{10x}{10}$

   2.25 = x

Answer 2

Answer:

$\large\boxed{x=\dfrac{9}{4}=2\dfrac{1}{4}}$

Step-by-step explanation:

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