Solve the quadratic equation by factoring: 6x²−x=15

-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.

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

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

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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.

8 0

3 years ago

The coordinates below are the three vertices of a rectangle. Identify the fourth coordinate and the area of the rectangle.

blagie [28]

Answer:

(2,2), 24 units squared

Step-by-step explanation:

D is at (2,2) because it would make Line AD equal to line BC and line AB equal to line CD, which would make a rectangle.

Area= length x width

A= 6 x 4

A=24 units squared

Good Luck!

8 0

3 years ago

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Find two integers whose sum is -2 and product is -24

il63 [147K]

Answer:

-6,4

Step-by-step explanation:

-6 times 4 is -24. -6 plus 4 is -2

3 0

3 years ago

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What is the value of X in the figure? X=??

snow_lady [41]

Answer:

29°

Step-by-step explanation:

SMH sorry it wasnt $\ 21$

8 0

3 years ago

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if a 100 n weight sits on a scale in a express elevator, what will happen to the weight shown on the scale when the elevator acc

Whitepunk [10]

Answer:

The phrasing of the question is weird, but the mass should not change. The scale may read higher for a moment, but once the mass is brought up to the same velocity of the elevator, it should settle back to 100.

4 0

3 years ago