9) X value range [-2/5,0] or [2,3]
b since I can't see a or c visablely) x>1
5) -5/3 ≤ x ≤ 2
6) The time interval by which the ball spends more than 1.5m above ground is about 0.263 <x< 1.166 seconds so about 1.397 seconds
9) To find the range of x value, you have to find the interception of these two solutions, and to do that, you have to find each of their solutions
To find the solution to 2x² ≥ 4x, you would first subtract 4x on both sides, resulting in 2x² - 4x ≥ 0. Then, you would factor to common terms, which are x and -2, the new inequality is 2x (x-2) ≥ 0. Then, you divide both 2x and 0 by 2. The new inequality is x (x-2) ≥ 0; you would then make everything ≥ 0. The solution is [- inf, 0] or [2, inf] for 5x² -13x -6 ≤ 0 you are basically doing the same thing for solving x which result in -2/5 ≤ x ≤ 3. With that said you find the interception of those 2 solutions which are [-2/5,0] and [2,3]. The first image should have a picture of the steps and a graph version of the work
b) To find the answer to x - 1/ (x+2) (x+3) > 0 you multiply both sides by (x+2) (x+3) you would then get x - 1 > 0. To islolate x you add 1 on both sides the final answer is x > 1
5) To solve 2x² + 3x + 1 ≤ 11x + 4x - x² you move 11x + 4x - x² on one side and simplify you would get 3x²
-x−10≤0. Then you split the second term into two terms which are 5x and -6x -> 3x² + 5 x - 6x - 10 ≤ 0 then you factor out the common terms in the terms you would then get (3x+5) (x-2) ≤ 0. Then you solve for x you would then get - 5/3 ≤ x ≤ 2. The new graph should show the solutions in graph form.
6) The first step is to create an inequality for the problem in this case it would be 7t - 4.9t > 1.5. At this point you move 1.5 on the left side to make 7t - 4.9t - 1.5 > 0 you would then multiply all terms on both sides by -1 to make -1.5 positive you would then get in standerd form 4.9t² -7t + 1.5 < 0. You would then factor with the quadratic formula after doing so you would get in its simplest form is (x - 1.166) (x - 0.263) < 0 then you would solve for x the time intervals that satisfy the scenario is about 0.263 ≤ x ≤ 1.166 then fine the difference between the solutions and that is about 1.937 seconds. The graph version is in the last picture.