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 (-0.5x - 1.6 = -2.9x)

d (2.3x + 1.3 = 8.8)

e (2.3x = 10.4 - 2.9x)

Explanation:

⚡ Using what you learned: solving linear equations in one variable

Step 1: Analyze the original equation

The given equation is:

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

To find valid first steps, we can apply properties of equality (adding, subtracting, multiplying, or dividing the same value on both sides).

Step 2: Evaluate Option A and Option E

Add \( 1.6 \) to both sides of the equation:

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

$$ 2.3x = 10.4 - 2.9x $$

• This matches Option E.
• Option A is incorrect because it has a minus sign instead of an equals sign: \( 2.3x - 10.4 = -2.9x \).

Step 3: Evaluate Option B

Add \( 2.9x \) to both sides of the equation:

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

$$ 5.2x - 1.6 = 8.8 $$

• This matches Option B.

Step 4: Evaluate Option C

Subtract \( 8.8 \) from both sides of the equation:

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

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

(This does not match Option C, which is \( -0.5x - 1.6 = -2.9x \)).

Step 5: Evaluate Option D

Subtract \( 2.3x \) from both sides of the equation:

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

$$ -1.6 = 8.8 - 5.2x $$

(This does not match Option D).

Answer:

The correct options are:

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