Solve for x: 20x + 10x = 100.

Step-by-step solution

1. 1

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

   $20x+10x=(20+10)x=30x$

   The equation becomes

   $30x=100$

2. 2

   Divide both sides by 30.

   $x=\frac{100}{30}$

3. 3

   Reduce the fraction. Numerator and denominator share the factor $10$:

   $\frac{100}{30}=\frac{100\div10}{30\div10}=\frac{10}{3}$

   Leaving the answer as $\tfrac{100}{30}$ is not wrong arithmetically but is not in lowest terms, which is usually what is asked for.

4. 4

   Give the decimal, and note it does not terminate.

   $x=\frac{10}{3}=3.\overline{3}\approx3.33$

   Because the denominator $3$ is not built only from $2$s and $5$s, the decimal repeats forever — so the fraction is the exact answer.

5. 5

   Verify by substitution. $20\cdot\tfrac{10}{3}+10\cdot\tfrac{10}{3}=\tfrac{200}{3}+\tfrac{100}{3}=\tfrac{300}{3}=100$ ✓, exact in fraction arithmetic with no rounding.