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

Step-by-step solution

1. 1

   Simplify the coefficient before anything else. Reducing the first fraction by $20$:

   $\frac{2000}{180}=\frac{100}{9},$

   and then multiplying by $\tfrac53$:

   $\frac{100}{9}\cdot\frac53=\frac{500}{27}.$

   Combining the two fractions into one now means only a single reciprocal has to be handled at the end.

2. 2

   Rewrite the equation. It becomes

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

   Before solving, predict the sign: the left side exceeds $2210$, so the subtracted term must be negative, which forces $X<0$. Having that expectation makes a sign slip easy to catch.

3. 3

   Isolate the term containing $X$. Subtracting $2210$ from both sides:

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

4. 4

   Divide by the fractional coefficient. Dividing by $-\tfrac{500}{27}$ is multiplying by $-\tfrac{27}{500}$:

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

   The fraction reduces by $10$; note $513=27\times19$ and $50=2\times5^{2}$ share no factor, so $-\tfrac{513}{50}$ is the exact value in lowest terms.

5. 5

   Substitute back. With $X=-10.26$:

   $\frac{500}{27}\times(-10.26)=-190,\qquad 2210-(-190)=2400 ✓.$

   The negative answer matches the sign prediction made in step 2.