Question

PLSSSHELP ASAP Determine which integers in the set S:{−40, −10, 20, 40} will make the inequality one fifth times the difference of m and five is less than or equal to one tenth times the difference of m and twenty false.
S:{−40, −10}
S:{−10, 20}
S:{20, 40}
S:{−40, 40}

Answer 1

Answer:

C)  S: {20, 40}

Step-by-step explanation:

Given inequality:

$\dfrac{1}{5}(m-5)\leq \dfrac{1}{10}(m-20)$

To solve the inequality, multiply both sides by 10:

$\implies \dfrac{10}{5}(m-5)\leq \dfrac{10}{10}(m-20)$

$\implies2(m-5)\leq m-20$

Expand the left side:

$\implies 2m-10 \leq m-20$

Subtract m from both sides:

$\implies m-10 \leq -20$

Add 10 to both sides:

$\implies m \leq -10$

Therefore, the true solution set to the given inequality are values of m that are less than or equal to -10.  

Therefore, the integers in the given set that make the inequality false are the values of m that are greater than -10:

• S: {20, 40}