Question

solve the inequality. explain how you found your answer.
6(x - 2) - 3 ≥ -3(-2 + 9) + 7

what is the best first step to solve the given inequality?
a. apply the multiplication or division property of inequality
b. combine like terms where possible
c. apply the addition or subtraction property of inequality
d. apply the distributive property

combine like terms and simplify
6(x - 2) - 3 ≥ -3(-2 + 9) + 7
6(x - 2) - 3 ≥ \boxed{?}
(type an integer or a fraction.)

Explanation:

Step1: Simplify the right - hand side

First, we simplify the expression inside the parentheses on the right - hand side: \(-2 + 9=7\).
Then we multiply by \(-3\): \(-3\times7=-21\).
Next, we add 7 to this result: \(-21 + 7=-14\).

Step2: Determine the simplified right - hand side

So, after combining like terms and simplifying the right - hand side of the inequality \(6(x - 2)-3\geq-3(-2 + 9)+7\), we get \(6(x - 2)-3\geq - 14\).

Answer:

• For the first - step question: D. Apply the Distributive Property (Note: Actually, the first step to simplify the right - hand side is to combine like terms inside the parentheses first, but among the given options, to solve the inequality \(6(x - 2)-3\geq-3(-2 + 9)+7\), the first step for the left - hand side is to apply the distributive property \(a(b + c)=ab+ac\) to \(6(x - 2)\) and for the right - hand side, we first combine like terms inside the parentheses. But if we consider the left - hand side, the first step is to apply the distributive property. However, for the right - hand side simplification, we first combine like terms inside the parentheses. But according to the options, the best first step to start solving the inequality (to expand and simplify both sides) is to apply the distributive property to \(6(x - 2)\) on the left and simplify the parentheses on the right. But the question about the first step: the right - hand side has \(-2 + 9\) which is combining like terms, but the left - hand side has \(6(x - 2)\) which needs the distributive property. So the answer for the first step question is D.
• For the simplification of the right - hand side: \(-14\)