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

C) S: {20, 40}

Explanation:

Given inequality:

`(1)/(5)(m-5)\leq (1)/(10)(m-20)`

To solve the inequality, multiply both sides by 10:

`\implies (10)/(5)(m-5)\leq (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}