Question

question
select the values that make the inequality $7m \geq 0$ true. then write an equivalent inequality, in terms of $m$.
(numbers written in order from least to greatest going across.)

answer attempt 1 out of 2

-10 -5 -3
-1 0 1
3 5 10
equivalent inequality: $m$ \boxed{1}

Explanation:

Step1: Solve the inequality \(7m \geq 0\)

To solve for \(m\), we divide both sides of the inequality by 7 (since 7 is positive, the direction of the inequality sign remains the same). So we have \(\frac{7m}{7} \geq \frac{0}{7}\), which simplifies to \(m \geq 0\).

Step2: Identify values that satisfy \(m \geq 0\)

Now we check each number:

• \(-10\): \( -10 < 0\), so it does not satisfy.
• \(-5\): \( -5 < 0\), so it does not satisfy.
• \(-3\): \( -3 < 0\), so it does not satisfy.
• \(-1\): \( -1 < 0\), so it does not satisfy.
• \(0\): \(0 = 0\), so it satisfies.
• \(1\): \(1 > 0\), so it satisfies.
• \(3\): \(3 > 0\), so it satisfies.
• \(5\): \(5 > 0\), so it satisfies.
• \(10\): \(10 > 0\), so it satisfies.

Answer:

The values that make the inequality true are \(0\), \(1\), \(3\), \(5\), \(10\). The equivalent inequality is \(m \geq 0\).