Determine the zeros of the function 7x^2 + 9x = 0

answers were:
{-9/7}
{-9/7,0}
{o,9/7}
{9/7}

I think the answer is {-9/7,0} but I'm not positive when I worked it-If this is wrong please steer me into the correct calcs because then I don't what I'm doing wrong

2.Solution to absolute value(x-5) <= 3 is x<=8>=2
This would be true according to my calcs Thanks for checking in advance

1. (-9/7, 0)

you are correct

2. correct, but should be written as
2 <= x <= 8

To determine the zeros of the function 7x^2 + 9x = 0, we need to find the values of x for which the function equals zero. We can do this by factoring out the common factor of x:

7x(x + 9/7) = 0

Now we have two factors: 7x = 0 and x + 9/7 = 0.

- For 7x = 0, we can divide both sides by 7 to isolate x: x = 0.
- For x + 9/7 = 0, we can subtract 9/7 from both sides to isolate x: x = -9/7.

So, the zeros of the function 7x^2 + 9x = 0 are x = 0 and x = -9/7.

Therefore, the correct answer is {-9/7, 0}.

For the second question, you are asked to find the solution to the inequality absolute value(x-5) ≤ 3.

To solve this inequality, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: x - 5 ≥ 0 (x is greater than or equal to 5)
In this case, the absolute value becomes x - 5, and the inequality becomes:
x - 5 ≤ 3

To solve this inequality, we add 5 to both sides:
x ≤ 3 + 5
x ≤ 8

So, if x is greater than or equal to 5, the solution is x ≤ 8.

Case 2: x - 5 < 0 (x is less than 5)
In this case, the absolute value becomes -(x - 5), and the inequality becomes:
-(x - 5) ≤ 3

To solve this inequality, we multiply both sides by -1 (which reverses the inequality):
x - 5 ≥ -3

Then, we add 5 to both sides to isolate x:
x ≥ -3 + 5
x ≥ 2

So, if x is less than 5, the solution is x ≥ 2.

Combining these two cases, we can say that the solution to the inequality absolute value(x - 5) ≤ 3 is x ≤ 8 and x ≥ 2.

Therefore, your calculations are correct, and the answer x ≤ 8 and x ≥ 2 is accurate.