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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}

Respuesta :

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:

[tex](x-3)\leq 0\\(x+5) \leq0[/tex]

For the inequality;

[tex]x-3\leq0\\x\leq0+3\\x\leq3[/tex]

For the inequality x+5≤0

[tex]x+5\leq 0\\x \leq -5\\[/tex]

Combining the inequalities:

[tex]-5 \leq x \leq 3[/tex]

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

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

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