explain why the inequality (x-4)^2<0 has exactly one solution(you may use graphi

Question

explain why the inequality (x-4)^2<0 has exactly one solution(you may use graphing approach, but are not required to.) Group Problem 3 1. Use graphing approach to solve the inequalityx+2x-80 (a) Graph the function f(x)x+2r-8, find and label x-intercepts, shade the solution set on the x-axis Hint:x)+2x-8-+ -9 (b) Write down the solution set using an interval notation; compare your answer with the answer of other group members. (c) Which of the following numbers belong to the solution set? Does your result support or contradict with your answer to part (b)? 10,-5,-4,-2, 0,1,2,3, 100 (d) Write down the solution set to the inequality +2x-8s0 2. (a) Explain why the inequality (x-4 graphing approach, but are not required to) S0 has exactly one solution (you may use (b) What is this solution? (c) Does the inequality (-4) 2 0also have exactly one solution? (d) which of the following numbers are the solutions of the inequality ( 20? 10,-5,4,-2,0,1,23 3. Explain why the inequality (x-2)>0 has one real number which is not a solution. What is this number? Give examples of numbers which satisfy the inequality Which is a cormect statement? (Oustify your answer): (a) The inequality x-x+1>0 has no solution (b) The inequalityx-x+1>0 has in finitely many solutions

Explanation / Answer

(x-4)2<=0

square of any value whether its a positive or negative, the result is always positive. It means the value of the result of the square is never less than 0.

So for (x-4)2<=0, the only solution is x=0

If it is (x-4)2>=0, then in that case we have many solutions.

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