Question

927. Используя координатную прямую, найдите объединение число- вых промежутков: 1) (-12; 8] и [5; 11); 4) (-2; 3] и [6; 10); 2) (-со; -3) и [-5; 4); 5) [-7; -1] и [-3; 7]; 3) [2; +оо) и (7; +оо); 6) (-ор; 1) и (-4; 10). Пж ПОМОГИТЕ ПОЖАЛУЙСТА СРОЧНО!​

Answer 1

1) (-12; 8] ∪ [5; 11)=(-12;11);

4) (-2; 3]∪ [6; 10=(-2;10);

2) (-∞; -3) ∪ [-5; 4)=(-∞; 4);

5) [-7; -1] ∪ [-3; 7]= [-7; 7]

3) [2; +оо) ∪ (7; +оо)= [2; +оо);

6) (-ор; 1) ∪ (-4; 10)= (-ор; 10).

Answer 2

Finding the Union of Intervals Using a Number Line

To find the union of intervals using a number line, we need to identify the overlapping or adjacent intervals and combine them into a single interval. Let's solve the given problem step by step:

1) (-12; 8] and [5; 11) - The first interval is from -12 to 8 (inclusive at 8). - The second interval is from 5 to 11 (exclusive at 11). - Since there is no overlap or adjacency between these intervals, we represent the union as (-12; 8] U [5; 11).

2) (-2; 3) and [6; 10) - The first interval is from -2 to 3 (exclusive at -2 and inclusive at 3). - The second interval is from 6 to 10 (exclusive at 10). - Since there is no overlap or adjacency between these intervals, we represent the union as (-2; 3) U [6; 10).

3) (-∞; -3) and [-5; 4) - The first interval is from negative infinity to -3 (exclusive at -3). - The second interval is from -5 to 4 (exclusive at 4). - Since there is an overlap between these intervals, we combine them into a single interval: (-∞; -3) U [-5; 4).

4) [-7; -1] and [-3; 7] - The first interval is from -7 to -1 (inclusive at -7 and -1). - The second interval is from -3 to 7 (inclusive at -3 and 7). - Since there is an overlap between these intervals, we combine them into a single interval: [-7; 7].

5) [2; ∞) and (7; ∞) - The first interval is from 2 to positive infinity (inclusive at 2). - The second interval is from 7 to positive infinity (exclusive at 7). - Since there is no overlap or adjacency between these intervals, we represent the union as [2; ∞).

6) (-∞; 1) and (-4; 10) - The first interval is from negative infinity to 1 (exclusive at 1). - The second interval is from -4 to 10 (exclusive at -4 and 10). - Since there is an overlap between these intervals, we combine them into a single interval: (-∞; 10).

Therefore, the union of the given intervals is:

(-12; 8] U [5; 11) U (-2; 3) U [6; 10) U (-∞; -3) U [-5; 4) U [-7; 7] U [2; ∞) U (-∞; 10).

Please note that the notation (-∞; x) represents all real numbers less than x, and (x; ∞) represents all real numbers greater than x.

I hope this helps! Let me know if you have any further questions.