A. Solve the following rational equations.Note that your solutions will be graded based on the correctness of your LCD (1 point), correctness of the steps prior to the final answer (1 point), correctness of the solutions/roots (1 point) and correctness of the checking part (1 point). (20 points)

1. x   =   10
   -----       -----
  x + 2     15

Solution Answer: 

Checking:

Let's solve the given rational equation step by step:

### The given equation is:

\[
\frac{x}{x + 2} = \frac{10}{15}
\]

### Step 1: Simplify the equation.
First, simplify the right-hand side of the equation:
\[
\frac{10}{15} = \frac{2}{3}
\]

So the equation becomes:
\[
\frac{x}{x + 2} = \frac{2}{3}
\]

### Step 2: Cross-multiply.
To eliminate the denominators, we can cross-multiply:
\[
x \cdot 3 = (x + 2) \cdot 2
\]

This simplifies to:
\[
3x = 2(x + 2)
\]

### Step 3: Expand the right side.
Expand the right-hand side of the equation:
\[
3x

Solve the following rational equations. Note that your solutions will be graded based on the correctness of your LCD (1 point), correctness of the steps prior to the final answer (1 point), correctness of the solutions/roots (1 point), and correctness of the checking part (1 point). (20 points)

1. x / (x + 2) = 10 / 15

This page explains how to solve the rational equation x / (x + 2) = 10 / 15 step by step. Learn how to simplify fractions, use cross-multiplication, and check the correctness of your solutions. Ideal for students in Grades 8-10.

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