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Ivan
2 years ago
13

Solve |2x - 6| > 10

Mathematics
1 answer:
sashaice [31]2 years ago
4 0

\text{Solve the absolute value:}\\\\\text{(Remember, there are two outcomes)}\\\\\text{First outcome:}\\\\2x - 6 > -10\\\\\text{Add 6 to both sides}\\\\2x>-4\\\\\text{Divide:}\\\\x 10\\\\\text{Add 6 from both sides}\\\\2x>16\\\\\text{Divide both sides by 2}\\\\x>8\\\\\boxed{\text{Answer: B.}\,{x|x < -2 \,or \,x > 8}}

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<u>Question:</u>

Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0

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The number of real solutions for the equation x^{2}+5 x+7=0 is zero

<u>Solution:</u>

For a Quadratic Equation of form : a x^{2}+b x+c=0  ---- eqn 1

The solution is x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}  

Now , the given Quadratic Equation is x^{2}+5 x+7=0  ---- eqn 2

On comparing Equation (1) and Equation(2), we get

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In x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} , b^2 - 4ac is called the discriminant of the quadratic equation

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Now, here are the rules with discriminants:

1) D > 0; there are 2 real solutions in the equation

2) D = 0; there is 1 real solution in the equation

3) D < 0; there are no real solutions in the equation

Now let solve for given equation

D= b^2 - 4ac\\\\D = 5^2 - 4(1)(7)\\\\D = 25 - 28 \\\\D = -3

Since -3 is less than 0, this means that there are 0 real solutions in this equation.

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