Solve the equation 20x + 10x = 2000.

Step-by-step solution

1. 1

   Combine the like terms on the left. Both terms are multiples of $x$, so add their coefficients:

   $20x+10x=(20+10)x=30x\quad\Longrightarrow\quad 30x=2000$

2. 2

   Divide both sides by $30$.

   $x=\frac{2000}{30}$

3. 3

   Reduce the fraction fully. The greatest common divisor of $2000$ and $30$ is $10$:

   $\frac{2000}{30}=\frac{200}{3}$

   Since $3$ does not divide $200$, this is the simplest exact form.

4. 4

   Report the decimal as an approximation only. $\tfrac{200}{3}=66.\overline{6}$, so writing $x\approx 66.67$ is a rounded value, not the answer. Rounding here loses information and would make the check fail slightly.

5. 5

   Check with the exact fraction.

   $30\cdot\frac{200}{3}=\frac{6000}{3}=2000\qquad\checkmark$