Theodore H. answered • 01/10/21
Math Professor, PhD in Math Education, MS in Math/Statistics
Compound inequalities express two distinct inequalities. In this case 4 ≤ 1/3x + 7 ≤ 10 represents the inequalities 4 ≤ 1/3x + 7 AND 1/3x + 7 ≤ 10. As such, the processes used to solve each individual inequality can be applied to the compound inequality. Here are the solution steps and justifications:
4 ≤ 1/3x + 7 ≤ 10
4 - 7 ≤ 1/3x + 7 - 7 ≤ 10 - 7 (Subtract 7 from each expression)
-3 ≤ 1/3x ≤ 3 (Simplify)
3(-3) ≤ 3(1/3x) ≤ 3(3) (Multiply each expression by 3)
-9 ≤ x ≤ 9 (Simplify)
So, the solution to the compound inequality is -9 ≤ x ≤ 9
Angie G.
please01/10/21
Maya V.
Similarly to what Theodore did above, we subtract 4 on both sides for the first one, to get x singled out on one side: x+4-4>=4-4 The answer: x>=0 And for the second expression we again need to subtract 6 from both sides to get x on one side and a new number on the other: x+6-6<=5-6 The answer: x<=-101/10/21
Angie G.
can you please help me with another question? x + 4 ≥ 4 and x + 6 ≤ 501/10/21