Respuesta :

Answer:

Hello!!

Solving for the equation [tex]3x^{2} +10x-8\leq 0[/tex]

The answer in interval notation is [tex][-4, \frac{2}{3} ][/tex]

The answer in inequality form is [tex]-4\leq x\leq \frac{2}{3}[/tex]

Step-by-step explanation:

Solve the inequality by finding the roots and creating test intervals

Hope this helps!!

lxg784

Answer:

−4 ≤ x ≤ 2/3

Step-by-step explanation:

Let's solve your inequality step-by-step.

3x^2 + 10x − 8 ≤ 0

Let's find the critical points of the inequality.

3x^2 + 10x − 8 = 0

(3x − 2)(x + 4) = 0(Factor left side of equation)

3x − 2 = 0 or x + 4 = 0 (Set factors equal to 0)

x = 2/3 or x=−4

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x ≤ − 4(Doesn't work in original inequality)

−4 ≤ x ≤ 2/3

(Works in original inequality)

x ≥ 2/3

(Doesn't work in original inequality)

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