# How do you solve the inequality #6x^2-5x>6#?

I would start by solving it as a normal equation (2nd degree). So you write:

Solving your equation you should get two values

Now the tricky bit:

your inequality asks you for values of

They cannot be

Graphically your function gives the following parabola:

graph{6x^2-5x-6 [-11.96, 13.02, -7.14, 5.34]}

So, basically I have to choose values that are outside the boundaries formed by the two values

Consider

If I put

Consider now

If I put

So, OUTSIDE the interval bound by

You express this by writing your solution as:

Or graphically

Hope it helps

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To solve the inequality (6x^2 - 5x > 6), you first need to rearrange it to form a quadratic inequality in standard form. This means bringing all terms to one side of the inequality sign and setting the expression equal to zero.

(6x^2 - 5x - 6 > 0)

Now, you have a quadratic inequality in the form (ax^2 + bx + c > 0).

To solve this type of quadratic inequality, you can use various methods, such as factoring, graphing, or the quadratic formula. One common approach is to find the critical points by solving the related equation (6x^2 - 5x - 6 = 0) and then test intervals to determine where the inequality holds true.

To find the critical points, you can use the quadratic formula:

(x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}})

Substitute (a = 6), (b = -5), and (c = -6) into the quadratic formula and solve for (x):

(x = \frac{{-(-5) \pm \sqrt{{(-5)^2 - 4 \cdot 6 \cdot (-6)}}}}{{2 \cdot 6}})

After calculating, you'll find two solutions for (x).

Once you have the critical points, you can use them to create intervals on the number line and test each interval to see where the inequality holds true. You can use test points within each interval to determine whether the expression is greater than zero or not. The intervals where the expression is greater than zero will be the solution to the inequality.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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