Question

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Determine which integers in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false.

S:{16, 32}
S:{−8, 16}
S:{−32, −8}
S:{−32, 32}

1. Inequality shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
The integer that can make the inequality true is m = -8
(1/4)(m – 4) ≤ (1/8)(m – 16)
1/4 x -12 ≤ 1/8 x -24
-3 ≤ -3

### What is inequality?

It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
One-fourth times the difference between m and four is less than or equal to oneeighth times the difference between m and sixteen
This can be written as,
(1/4)(m – 4) ≤ (1/8)(m – 16)
The number that will make the inequality true.
S = {−32, −8, 16, 32}
We will check each value.
m = -32
1/4 x -36 ≤ 1/8 x -48
-9 ≤ -4
Not true
m= -8
1/4 x -12 ≤ 1/8 x -24
-3 ≤ -3
True
m = 16
1/4 x 12 ≤ 1/8 x 0
3 ≤ 0
Not true
m = 32
1/4 x 28 ≤ 1/8 x 16
7 ≤ 2
Not true
Thus,
The integer that can make the inequality true is m = -8
(1/4)(m – 4) ≤ (1/8)(m – 16)
1/4 x -12 ≤ 1/8 x -24
-3 ≤ -3
Learn more about inequalities here:
#SPJ2

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