The solution of the equation is x = -4/3.
<h3>What does it mean to solve an equation?</h3>
An equation represents equality of two or more mathematical expression.
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
WE have been given an equation as;
|x - 4| = 5x + 12
In an absolute value equation, we solve the original expression as our first equation. Our second one is that we multiply the right side by -1.
Case 1: original equation
|x - 4| = 5x + 12
x - 4 = 5x + 12
x - 5x = 12 + 4
-4x = 16
x = -4
Case 2: Opposite equation
|x - 4| = 5x + 12
x - 4 = - (5x + 12)
x - 4 = - 5x - 12
x + 5x = -12 + 4
6x = -8
x = -4/3
Now we have two solutions. We need to check for extraneous solutions because of all the manipulations;
Check:
|x - 4| = 5x + 12
use x = -4
|-4 - 4| = 5(-4) + 12
| -8 | = -20 + 12
8 = -8
Thus, it is Not a solution
Now, |x - 4| = 5x + 12
use x = -4/3
| -4/3 - 4| = 5( -4/3) + 12
|-16/3 | = -20/3 + 12
|-16/3 | = 16/3
16/3 = 16/3
Thus, it is the Solution.
Learn more about solving equations here:
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Answer:
28
Step-by-step explanation:
Answer:
840.32
Step-by-step explanation:
Answer:
The answer is below
Step-by-step explanation:
Select the quadrant in which the terminal side of the angle falls.
210° terminates in quadrant
-150° terminates in quadrant
390° terminates in quadrant
Solution:
The x and y axis divides the cartesian plane into four equal parts known as the four quadrants.
Angles between 0° and 90° are in the first quadrant, angles between 90° and 180° are in the second quadrant, angles between 180° and 270° are in the third quadrant while angles between 270° and 360° are in the fourth quadrant.
a) Since 210 degrees is between 180° and 270°, hence it terminates in the third quadrant.
b) -150° = 360 - 150 = 210°. Since 210 degrees is between 180° and 270°, hence it terminates in the third quadrant.
c) 390° = 390° - 360° = 30°.
Since 30 degrees is between 0° and 90°, hence it terminates in the first quadrant.
