# For which of the following values of x the inequality x (x + 3) < 10 is satisfied?

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The equation = x(x+3) <10

Try the values of X from 0

When x=0, 0(0+3) = 0<10 satisfies the equation.

When x=1, 1(1+3) = 1(4) = 4< 10 satisfies the equation.

When x=2, 2(2+3) = 2(5) = 10 not less than 10

So the values of X that satisfies the equation are 0 and 1.

The given inequality is x (x + 3) < 10

In order to solve the above inequality, we need to find the values of x.

x (x + 3) = 10

⇒ x2 + 3x = 10

⇒ x2 + 3x – 10 = 0

⇒ (x – 2)(x + 5) = 0

⇒ x = 2 or x = -5

Therefore, the values of x satisfying the given inequality are 2 and -5.

The given inequality is x (x + 3) < 10

⇒ x2 + 3x < 10

⇒ x2 + 3x – 10 < 0

⇒ (x – 2)(x + 5) < 0

Now we solve this by checking the positive and negative values of the inequality

For x < -5, the LHS>0. So not feasible solution.

For -5<x<2, the LHS<0. So it is a feasible solution.

For x>2, the LHS>0. So not feasible solution.

Therefore, the values of x satisfying the given inequality are between -5 and 2.