The inequality which can bee represented on the number line.
B. 2|x + 1| ≤ 8
D. 2|x − 1| ≤ 10
Given, the inequalities are:
A. |2x + 1| ≥ 7
2x+1≥7 or -2x-1≥7
2x≥7-1 or -2x≥7+1
2x≥6 or -2x≥8
x≥6/2 or x≤-8/2
x≥3 or x≤-4
therefore, (-∞,-4]∪[3,∞)
hence this inequality cannot be represented on the number line.
B. 2|x + 1| ≤ 8
2x+2≤8 or -2x-2≤8
2x≤8-2 or -2x≤8+2
2x≤6 or -2x≤10
x≤3 or x≥-5
-5≤x≤3
[-5,3]
hence this inequality can be represented on the number line.
C. |2x − 1| ≥ 9
2x-1≥9 or -2x+1≥9
2x≥9+1 or -2x≥9-1
2x≥10 or -2x≥8
x≥5 or x≤-4
(-∞,-4]∪[5,∞)
hence this inequality cannot be represented on the number line.
D. 2|x − 1| ≤ 10
2x-2≤10 or -2x+2≤10
2x≤10-2 or -2x≤10+2
2x≤8 or -2x≤12
x≤4 or x≥-6
-4≤x≤6
[-5,3]
hence this inequality can be represented on the number line.
Hence we get the required results.
Learn more about Inequality here:
brainly.com/question/25275758
#SPJ1
