Question

alicia is solving the equation (2.3x - 1.6 = 8.8 - 2.9x). which equations represent possible ways to begin solving for (x)?

check all that apply.

a (2.3x - 10.4 = -2.9x)
b (5.2x - 1.6 = 8.8)
c (-6.5x - 1.6 = -2.9x)
d (2.3x + 1.3 = 8.8)
e (2.3x = 10.4 - 2.9x)

Explanation:

⚡ Using what you learned: Solving Equations with Variables on Both Sides

Step 1: Analyze the original equation

The original equation is:

$$ 2.3x - 1.6 = 8.8 - 2.9x $$

To find valid first steps, we can perform standard algebraic operations (addition or subtraction) on both sides of the equation.

Step 2: Test Option A and Option E (Moving constant terms)

If we subtract \( 8.8 \) from both sides:

$$ 2.3x - 1.6 - 8.8 = 8.8 - 2.9x - 8.8 $$

$$ 2.3x - 10.4 = -2.9x $$

This matches Option A.

If we add \( 1.6 \) to both sides:

$$ 2.3x - 1.6 + 1.6 = 8.8 - 2.9x + 1.6 $$

$$ 2.3x = 10.4 - 2.9x $$

This matches Option E.

Step 3: Test Option B and Option C (Moving variable terms)

If we add \( 2.9x \) to both sides:

$$ 2.3x - 1.6 + 2.9x = 8.8 - 2.9x + 2.9x $$

$$ 5.2x - 1.6 = 8.8 $$

This matches Option B.

If we subtract \( 2.3x \) from both sides:

$$ 2.3x - 1.6 - 2.3x = 8.8 - 2.9x - 2.3x $$

$$ -1.6 = 8.8 - 5.2x $$

This does not match Option C (which has \( -6.5x - 1.6 = -2.9x \)) or Option D.

Answer:

The correct options are:

• A \( 2.3x - 10.4 = -2.9x \)
• B \( 5.2x - 1.6 = 8.8 \)
• E \( 2.3x = 10.4 - 2.9x \)