Question

select the values that make the inequality $-d \leq 8$ true. then write an equivalent inequality, in terms of $d$. (numbers written in order from least to greatest going across.) answer attempt 1 out of 2 -13 -9 -8.1 -8 -7.9 -7 -3 0 3 7 7.9 8 8.1 9 13 equivalent inequality: $d$

Explanation:

Step1: Solve the inequality \(-d \leq 8\)

To solve for \(d\), we multiply both sides of the inequality by \(-1\). Remember that when we multiply or divide an inequality by a negative number, the direction of the inequality sign flips. So we have:
\(-d \times (-1) \geq 8 \times (-1)\)
Simplifying both sides, we get \(d \geq -8\).

Step2: Identify values of \(d\) that satisfy \(d \geq -8\)

We check each value:

• \(-13\): \(-13 < -8\) (does not satisfy)
• \(-9\): \(-9 < -8\) (does not satisfy)
• \(-8.1\): \(-8.1 < -8\) (does not satisfy)
• \(-8\): \(-8 = -8\) (satisfies)
• \(-7.9\): \(-7.9 > -8\) (satisfies)
• \(-7\): \(-7 > -8\) (satisfies)
• \(-3\): \(-3 > -8\) (satisfies)
• \(0\): \(0 > -8\) (satisfies)
• \(3\): \(3 > -8\) (satisfies)
• \(7\): \(7 > -8\) (satisfies)
• \(7.9\): \(7.9 > -8\) (satisfies)
• \(8\): \(8 > -8\) (satisfies)
• \(8.1\): \(8.1 > -8\) (satisfies)
• \(9\): \(9 > -8\) (satisfies)
• \(13\): \(13 > -8\) (satisfies)

Answer:

Values that make the inequality true: \(-8\), \(-7.9\), \(-7\), \(-3\), \(0\), \(3\), \(7\), \(7.9\), \(8\), \(8.1\), \(9\), \(13\)
Equivalent Inequality: \(d \geq -8\)