YouSir67
Answered

what are the solutions to the inequality (x-3)(x+5) ≤ 0

{x | 3 ≤ x ≤ 5}

{x | -5 ≤ x ≤ -3}

{x | -5 ≤ x ≤ 3}

{x | -3 ≤ x ≤ 5}

Verified Answer :

charlottekrist
  1. Solve for x
    x= 3 or x=-5

    2. From the values of x above, we have these 3 intervals to test
    x<=-5
    -5<=x<=3
    x<=3

    3. Pick a test point for each interval
    For the interval x<=-5:
    Lets pick x=-6. Then, (-6-3)(-6+5)<=0. After simplifying, we get 9<=0, which is false. So we drop this interval.

    For the interval -5<=x<=3:
    Lets pick x=0. Then (0-3)(0+5)<=0. After simplifying, we get -15<=0, which is true. So we keep this interval.

    For the interval x>=3:
    Lets pick x=4. Then, (4-3)/4+5)<=0. After simplifying, we get 9<=0, which is false. So we drop this interval.

    4. Therefore, 
    -5<=x<=3.
    The answer is therefore number 3 :D
abidemiokin

The solutions to the inequality (x-3)(x+5) ≤ 0 is {x | -5 ≤ x ≤ 3}

Given the inequality expression (x-3)(x+5) ≤ 0

This can also be expressed as:

\((x-3)\leq 0\\(x+5) \leq0\)

For the inequality;

\(x-3\leq0\\x\leq0+3\\x\leq3\)

For the inequality x+5≤0

\(x+5\leq 0\\x \leq -5\\\)

Combining the inequalities:

\(-5 \leq x \leq 3\)

Hence the solutions to the inequality (x-3)(x+5) ≤ 0 is {x | -5 ≤ x ≤ 3}

Learn more here: https://brainly.com/question/15816805

Related Questions