Solve the compound inequality:

(4 - x ≤ -1) ∩ (2 + 3x ≥ 17)

the upside down 'U' shape means intersection which means find the terms that are in both of the groups so for example (2,4,6,7) (upside down U shape) (3,5,7) the answer would be (7) because 7 is in both of the sets < means less than or equal to > means more than or equal to so so 4-x < -1 if we convert this to x=something then add x to both sides 4 < x-1 add 1 to both sides 5 < x
the second equation is 2+3x > 17 subtract 2 from both sides 3x > 15 divide both sides by 3 x > 5
so the intersection of 5 < x and x > 5 is 5 < x > 5 or 5 < x so the solution set is x={x|x > 5} or any number more than or equal to 5 will work

Answered by apologiabiology | 2024-06-10

The solution to the compound inequality (4 - x ≤ -1) ∩ (2 + 3x ≥ 17) is x ≥ 5. In interval notation, this is expressed as [5, ∞). Both inequalities yield the same solution, indicating all values of x greater than or equal to 5 satisfy both conditions.
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Answered by apologiabiology | 2024-11-18