Solve 2400 = 2210 - (2000/180)(5/3)X for X.

Step-by-step solution

1. 1

   Collapse the two fractions into one coefficient first. Reduce $\dfrac{2000}{180}$ by $20$:

   $\frac{2000}{180}=\frac{100}{9},\qquad \frac{100}{9}\cdot\frac{5}{3}=\frac{500}{27}$

   Working in exact fractions rather than $11.11\ldots$ keeps the final answer clean.

2. 2

   Rewrite the equation with the single coefficient.

   $2400=2210-\frac{500}{27}X$

3. 3

   Move the constant across. Subtracting $2210$ from both sides:

   $2400-2210=-\frac{500}{27}X\ \Longrightarrow\ 190=-\frac{500}{27}X$

   The left side is positive while the coefficient of $X$ is negative, so you already know $X<0$ before doing any arithmetic.

4. 4

   Divide by multiplying by the reciprocal.

   $X=190\cdot\left(-\frac{27}{500}\right)=-\frac{5130}{500}=-\frac{513}{50}=-10.26$

5. 5

   Check by substituting back. $\dfrac{500}{27}\times\left(-\dfrac{513}{50}\right)=-190$, so the right-hand side is $2210-(-190)=2400\ \checkmark$. The sign prediction from step 3 held.