Select the values that make the inequality start fraction, x, divided by, minus, 5, end fraction, ≤, minus, 4 /−5 x ≤−4 true. Then write an equivalent inequality, in terms of xx. (Numbers written in order from least to greatest going across.) Answer Attempt 1 out of 2 10 15 17 19 20 21 23 25 30
To solve the inequality $\frac{x}{-5} \leq -4$, we can multiply both sides by $-5$ to eliminate the fraction. However, when we multiply or divide by a negative number, we need to flip the inequality symbol. So, we have:
$x \geq (-4)(-5)$
$x \geq 20$
Therefore, the values that make the inequality true are $x = 20, 21, 23, 25, 30$.
Equivalent Inequality what is it
An equivalent inequality is an inequality that has the same solution set as the original inequality. In other words, if you replace the original inequality with an equivalent one, the set of values that make the inequality true remains the same.
no meant the problem
Apologies for the confusion. The equivalent inequality, in terms of $x$, for the inequality $\frac{x}{-5} \leq -4$ is $x \geq 20$.
Select the values that make the inequality start fraction, p, divided by, minus, 4, end fraction, ≤, 2
−4
p
≤2 true. Then write an equivalent inequality, in terms of pp.
(Numbers written in order from least to greatest going across.)
Answer
Attempt 1 out of 2
-16 -12 -11
-9 -8 -7
-5 -4 0
Equivalent Inequality: pp
Submit Answer
To solve the inequality $\frac{p}{-4} \leq 2$, we can multiply both sides by $-4$ to eliminate the fraction. Remember to flip the inequality symbol when multiplying or dividing by a negative number.
$-4 \cdot \frac{p}{-4} \geq 2 \cdot -4$
$p \geq -8$
Therefore, the values that make the inequality $-\frac{p}{4} \leq 2$ true are $-8$ and any number greater than $-8$.
The equivalent inequality, in terms of $p$, is $p \geq -8$.