Which set expresses the solution to the compound inequality −2≤2x+13−4<1 ? Responses {x:3≤x<7} left brace x colon 3 less-than-or-equal-to x less than 7 right brace {x:52≤x<7} left brace x colon Start Fraction 5 over 2 End Fraction less-than-or-equal-to x less than 7 right brace {x:−32≤x<1} left brace x colon Start Fraction negative 3 over 2 End Fraction less-than-or-equal-to x less than 1 right brace {x:52≤x<1}
The set that expresses the solution to the compound inequality is {x:−32≤x<1} or the interval -3/2 ≤ x < 1.
The correct set that expresses the solution to the compound inequality -2 ≤ 2x + 13 - 4 < 1 is {x: -3/2 ≤ x < 1}.
To find the solution to the compound inequality −2 ≤ 2x + 13 − 4 < 1, we need to solve it step by step.
First, let's simplify the inequality:
−2 ≤ 2x + 9 < 1
To isolate the term with x, we need to get rid of the constants. Subtracting 9 from all parts of the inequality:
−2 - 9 ≤ 2x + 9 - 9 < 1 - 9
-11 ≤ 2x < -8
Now, we need to isolate x by dividing all parts of the inequality by 2:
-11/2 ≤ (2x)/2 < -8/2
-11/2 ≤ x < -4
So, the solution to the compound inequality is {x: -11/2 ≤ x < -4}.