Question

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

6x ≥
(type an integer or a fraction.)
what is the best next step to solve the given inequality?
a. combine like terms where possible
b. apply the multiplication or division property of inequality.
c. apply the
d. apply the or subtraction property of inequality
apply the multi or division property of inequality.
6x
x
(type an integer or a fraction.)

Explanation:

Step1: Analyze the current inequality

We have the inequality \(6x \geq 1\) (assuming the first part was solved correctly to get here). The goal is to solve for \(x\). The term with \(x\) is \(6x\), so we need to isolate \(x\).

Step2: Determine the next step

To isolate \(x\) from \(6x\), we need to divide both sides of the inequality by \(6\) (or multiply by \(\frac{1}{6}\)). This is applying the Multiplication or Division Property of Inequality, which states that if we multiply or divide both sides of an inequality by a positive number, the direction of the inequality sign remains the same. Since \(6\) is positive, we can divide both sides by \(6\) to get \(x \geq \frac{1}{6}\).

For the multiple - choice question, the current inequality is \(6x\geq1\). To solve for \(x\), we need to get \(x\) alone. Since \(x\) is multiplied by \(6\), the next step is to apply the Multiplication or Division Property of Inequality (divide both sides by \(6\)). So the correct option is B. Apply the Multiplication or Division Property of Inequality.

Answer:

For the inequality \(6x\geq1\), the solution is \(x\geq\frac{1}{6}\). For the multiple - choice question, the answer is B. Apply the Multiplication or Division Property of Inequality.