Question

which is a correct first step in solving the inequality \\(-4(2x - 1) > 5 - 3x\\)?

• add 1 to both sides of the inequality.
• subtract \\(2x\\) from both sides of the inequality.
• distribute \\(-4\\) to get \\(-8x + 4 > 5 - 3x\\).
• distribute \\(-4\\) to get \\(-8x - 1 > 5 - 3x\\).

Explanation:

Identify the given inequality

We are given the following linear inequality to solve:

$$-4(2x - 1) > 5 - 3x$$

Apply the distributive property

Using the Distributive Property knowledge point

$$
LATEXBLOCK0
$$

Substitute back into the inequality

Using the Solving Linear Inequalities knowledge point

$$ -8x + 4 > 5 - 3x $$

Evaluate the given options

• "Add 1 to both sides of the inequality": Incorrect, as \(1\) is inside the parentheses and multiplied by \(-4\).
• "Subtract \(2x\) from both sides of the inequality": Incorrect, as \(2x\) is inside the parentheses.
• "Distribute \(-4\) to get \(-8x - 1 > 5 - 3x\)": Incorrect, because \(-4 \times -1 = +4\), not \(-1\).
• "Distribute \(-4\) to get \(-8x + 4 > 5 - 3x\)": Correct, as shown in our distribution step.

Answer:

• Add 1 to both sides of the inequality.
• Subtract \(2x\) from both sides of the inequality.
• Distribute \(-4\) to get \(-8x + 4 > 5 - 3x\). (Correct answer)
• Distribute \(-4\) to get \(-8x - 1 > 5 - 3x\).