The solution of the absolute inequality |y + 8| ≤ 2 is -10 ≤ y ≤ -6
<h3>What is an equation?</h3>An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.
Given the equation:
|y + 8| ≤ 2
Hence:
y + 8 ≤ 2; and -(y + 8) ≤ 2
y ≤ -6 and y ≥ -10
The solution of the absolute inequality |y + 8| ≤ 2 is -10 ≤ y ≤ -6
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Answer: a) see image (below)
b) S ∩ M = 237
c) S U M = 598
<u>Step-by-step explanation:</u>
b) Total students = 685
Not sports or music = 87
Sports Total = 385
Music Total = 450
Both Sports and Music is their intersection:
S ∩ M = S + M + N - T
= 385 + 450 + 87 - 685
= 237
c) Sports only = S - (S ∩ M)
= 385 - 237
= 148
Music only = M - (S ∩ M)
= 450 - 237
= 213
Sports OR Music is their union:
S U M = S + M - (S ∩ M)
= 385 + 450 - 237
= 598
