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3 years ago

What are the solutions to this equation? x² – 108 = 13 Pleasee HELP ASAP

Mathematics

1 answer:

PolarNik [594]3 years ago

6 0

Answer:11

Step-by-step explanation:

x^2-108 =13

+108 +108

x^2=121

2√x= √121

x=11

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

-3|9x-7|=2 Find the answer for x

labwork [276]

<h2>Solving Equations with Absolute Expressions</h2><h3>Answer:</h3>

No Solutions

<h3>Step-by-step explanation:</h3>

Given:

$-3|9x -7| = 2$

Rewriting the given equation:

$-3|9x -7| = 2 \\ |9x -7| = -\frac{2}{3}$

We have to realize that the right side of the equation, $|9x -7|$ , will always be positive no matter what real values of $x$ (because we're taking the absolute value of the expression) and we are equating it to a negative constant number, $-\frac{2}{3}\\$ . Something that is always positive will never be negative so there's no value for $x$ that satisfies the solution.

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You may not read the following passage that I have written.

$\rule{6.5cm}{0.5pt}$

Solving by positive of the expression:

$9x -7 = -\frac{2}{3} \\ 9x = -\frac{2}{3} +7 \\ 9x = -\frac{2}{3} +\frac{21}{3} \\ 9x = \frac{19}{3} \\ 9x \times \frac{1}{9} = \frac{19}{3} \times \frac{1}{9} \\ x = \frac{19}{27}$

Solving by the negative of the expression:

$-(9x -7)= -\frac{2}{3} \\ 9x -7 = \frac{2}{3} \\ 9x = \frac{2}{3} +7 \\ 9x = \frac{2}{3} +\frac{21}{3} \\ 9x = \frac{23}{3} \\ 9x \times \frac{1}{9} = \frac{23}{3} \times \frac{1}{9} \\ x = \frac{23}{27}$

Checking: $x = \frac{19}{27}\\$

$-3|9(\frac{19}{27}) -7| \stackrel{?}{=} 2 \\ -3|\frac{19}{3} -7| \stackrel{?}{=} 2 \\ -3|\frac{19}{3} -\frac{21}{3}| \stackrel{?}{=} 2 \\ -3|-\frac{2}{3}| \stackrel{?}{=} \\ -3(\frac{2}{3}) \stackrel{?}{=} 2 \\ -2 \stackrel{?}{=} 2 \\ -2 \neq 2$

$x = \frac{19}{27}\\$ is an extraneous solution.

Checking: $x = \frac{23}{27}\\$

$-3|9(\frac{23}{27}) -7| \stackrel{?}{=} 2 \\ -3|\frac{23}{3} -7| \stackrel{?}{=} 2 \\ -3|\frac{23}{3} -\frac{21}{3}| \stackrel{?}{=} 2 \\ -3|\frac{2}{3}| \stackrel{?}{=} \\ -3(\frac{2}{3}) \stackrel{?}{=} 2 \\ -2 \stackrel{?}{=} 2 \\ -2 \neq 2$

$x = \frac{23}{27}\\$ is an extraneous solution.

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Step-by-step explanation:

The one point where the lines intersect is one solution. If both points are on the same line it is one solution. If the lines do not intersect it is no solution.

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