Select the correct answer from each drop-down menu.Consider this equation.1𝑥+2𝑥+10=13Complete the statements to make them true.The least common denominator between all three fractions is .The equation will have valid solutions.

Sure, let's solve the equation step by step.

The given equation is: $\frac{1}{x} + \frac{2}{x} + 10 = 13$

Step 1: Combine the fractions on the left side. Since the denominators are the same (both are $x$), you can add the numerators directly: $\frac{1 + 2}{x} + 10 = 13$ $\frac{3}{x} + 10 = 13$

Step 2: Isolate the fraction term. Subtract 10 from both sides of the equation: $\frac{3}{x} = 3$

Step 3: Solve for $x$. Multiply both sides by $x$ to get rid of the fraction: $3 = 3x$

Divide both sides by 3: $x = 1$

Step 4: Verify the solution. Substitute $x = 1$ back into the original equation to ensure it satisfies the equation: $\frac{1}{1} + \frac{2}{1} + 10 = 13$ $1 + 2 + 10 = 13$ $13 = 13$

The solution is correct.

Now, let's complete the statements:

1. The least common denominator between all three fractions is $x$.
2. The equation will have 1 valid solution.

So, the completed statements are:

• The least common denominator between all three fractions is $x$.
• The equation will have 1 valid solution.