Question

practice test - aztecs ged® mathematical reasoning

hilary
\\5x + 3 - 3 = 2x + 18 - 3\\
\\5x = 2x + 15\\
\\5x - 2x = 2x - 2x + 15\\
\\3x = 15\\
\\\frac{3x}{3} = \frac{15}{3}\\
\\x = 5\\

rachel
\\5x - 5x + 3 = 2x - 5x + 18\\
\\3 = -3x + 18\\
\\3 - 18 = -3x + 18 - 18\\
\\-15 = -3x\\
\\\frac{-15}{-3} = \frac{-3x}{-3}\\
\\5 = x\\
\\x = 5\\

tracey
\\5x - 2x + 3 = 2x - 2x + 18\\
\\3x + 3 = 18\\
\\\frac{3x+3}{3} = \frac{18}{3}\\
\\x + 3 = 6\\
\\x + 3 - 3 = 6 - 3\\
\\x = 3\\

which student(s) solved the equation correctly?

a. rachel
b. hilary and rachel
c. tracey
d. hilary

Explanation:

⚡ Using what you learned: simplifying expressions · 🆕 New: Solving Multi-Step Equations
Finding the correct path to isolate a variable

Step 1: Analyze the original equation

To determine who solved the equation correctly, we first need to find the starting equation. Looking at the first line of each student's work, they are performing an operation on both sides of the same original equation:

$$ 5x + 3 = 2x + 18 $$

Let's solve this equation step-by-step to see which student's method is mathematically valid.

Step 2: Evaluate Hilary's work

Hilary starts by subtracting \( 3 \) from both sides:

$$ 5x + 3 - 3 = 2x + 18 - 3 $$

$$ 5x = 2x + 15 $$

Next, she subtracts \( 2x \) from both sides:

$$ 5x - 2x = 2x - 2x + 15 $$

$$ 3x = 15 $$

Finally, she divides both sides by \( 3 \):

$$ \frac{3x}{3} = \frac{15}{3} $$

$$ x = 5 $$

Every step Hilary took is mathematically correct and follows the properties of equality.

Step 3: Evaluate Rachel's work

Rachel starts by subtracting \( 5x \) from both sides:

$$ 5x - 5x + 3 = 2x - 5x + 18 $$

$$ 3 = -3x + 18 $$

Next, she subtracts \( 18 \) from both sides:

$$ 3 - 18 = -3x + 18 - 18 $$

$$ -15 = -3x $$

Finally, she divides both sides by \( -3 \):

$$ \frac{-15}{-3} = \frac{-3x}{-3} $$

$$ 5 = x $$

Every step Rachel took is also mathematically correct and follows the properties of equality.

Step 4: Evaluate Tracey's work

Tracey starts by subtracting \( 2x \) from both sides:

$$ 5x - 2x + 3 = 2x - 2x + 18 $$

$$ 3x + 3 = 18 $$

Next, she attempts to divide both sides by \( 3 \):

$$ \frac{3x + 3}{3} = \frac{18}{3} $$

On the left side, dividing the entire expression \( 3x + 3 \) by \( 3 \) should yield:

$$ \frac{3x}{3} + \frac{3}{3} = x + 1 $$

However, Tracey writes:

$$ x + 3 = 6 $$

She forgot to divide the constant term \( 3 \) by \( 3 \). This is an algebraic error, making her solution incorrect.

Step 5: Conclusion

Both Hilary and Rachel solved the equation correctly using mathematically sound steps.

Answer:

B