# Solve the equation. check for extraneous solutions. 9|9 – 8x| = 2x + 3

Solve the equation. check for extraneous solutions.

9|9 – 8x| = 2x + 3

## This Post Has 10 Comments

1. 544620 says:

81-72x=2x+3
81-3=2x+72x
78=74x
x=74/78
x=37/39 or 0.948...

To Check for extraneous solutions, you have to plug in the answers to the original equation. If it doesn’t work then it is extraneous and it is no solution

2. cat706 says:

81-72=2X+3
-3              -3

78-72=2X
6=2X
2/6=3
3=X

3. Loowkeychrissy7227 says:

39/37 and 6/5

Step-by-step explanation:

To start, let's assume that 9-8x is positive (we will do this to get rid of the absolute value, but then check later). We get 9(9 - 8x) = 2x + 3, or 81 - 72x = 2x + 3, so 74x = 78 and x = 39/37. If we assume 9-8x is negative, the |9-8x| will turn into 8x-9, so we get 9(8x - 9) = 2x + 3, or 72x - 81 = 2x + 3 , so 70x = 84 and x = 6/5. If we plug the values back in, 9-8(39/37) needs to be positive, which works, and 9-8(6/5) needs to be negative, and this works, so the answers are 39/37 and 6/5.

4. Anshuman2002 says:

The given equation is : 9|9-8x| = 2x + 3. Removing the modulus sign to get, 9(9-8x) = +2x+3 or 9(9-8x) = -2x-3 . Case 1: 9(9-8x) = +2x+3 or 81 -72x = 2x +3 or 78 = 74x or x = 78/74. Case 2:9(9-8x) = -2x-3 or 81 - 72x =- 2x -3 or 70x = 84 or x = 84/70. Thus, the solutions of x are 78/74 and 84/70. No, these are not extraneous solutions, as the answers are satisfying the equation.

5. lopezjose1530 says:

The solution of 9|9 – 8x| = 2x + 3 is 39/37 or 6/5

Further explanation

We need to recall the following definitions to solve absolute equation.

$| x - a | = \sqrt { (x - a)^2 }$

If | x | > a then x > a or x < -a

If | x | < a then -a < x < a

Let us tackle the problem.

This problem is about linear absolute equation.

Given:

$9 | 9 - 8x | = 2x + 3$

If x ≤ 9/8 , then :

$9 ( 9 - 8x ) = 2x + 3$

$81 - 72x = 2x + 3$

$81 - 3 = 72x + 2x$

$78 = 74x$

$x = 78 / 74$

$x = \boxed {\frac{39}{37}}$

If x > 9/8 , then :

$-9 ( 9 - 8x ) = 2x + 3$

$-81 + 72x = 2x + 3$

$-81 - 3 = -72x + 2x$

$-84 = -70x$

$x = -84 / -70$

$x = \boxed {\frac{6}{5}}$

Learn moreInfinite Number of Solutions : System of Equations : System of Linear equations : Answer details

Subject: Mathematics

Chapter: Absolute Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Absolute

$Solve the equation. check for extraneous solutions. 9|9 – 8x| = 2x + 3$

6. neariah24 says:

$9-8x\geq0\ \ \ |subtract\ 9\ from\ both\ sides\\\\-8x\geq-9\ \ \ \ |change\ signs\\\\8x\leq9\ \ \ \ |divide\ both\ sides\ by\ 8\\\\x\leq9\\\\ |9-8x|=\left\{\begin{array}{ccc}9-8x&for\ x\leq9\\8x-9&for\ x \ \textgreater \ 9\end{array}\right$

$1^o\ x\in(-\infty;\ 9]\to|9-8x|=9-8x\\\\9(9-8x)=2x+3\\81-72x=2x+3\ \ \ \ |subtract\ 81\ from\ both\ sides\\-72x=2x-78\ \ \ \ |subtract\ 2x\ from\ both\ sides\\-74x=-78\ \ \ \ |divide\ both\ sides\ by\ (-74)\\\\x=\dfrac{-78:2}{-74:2}\\\\\boxed{x=\frac{39}{37}}\in(-\infty;\ 9]$

$2^o\ x\in(9;\ \infty)\to|9-8x|=8x-9\\\\9(8x-9)=2x+3\\72x-81=2x+3\ \ \ \ |add\ 81\ to\ both\ sides\\72x=2x+84\ \ \ \ |subtract\ 2x\ from\ both\ sides\\70x=84\ \ \ \ \ \ |divide\ both\ sides\ by\ 70\\\\x=\dfrac{84:14}{70:14}\\\\x=\dfrac{6}{5}\notin(9;\ \infty)\\\\\\\boxed{x=\frac{39}{37}}$

7. JJJuliedavis says:

9|9-8x|=2x+3

As there is mod, there would be two solutions, one for +ve value and other for -ve valueIt will lead into either

1) 9(9-8x)=2x+3   OR
2) 9(9-8x)=-(2x+3)
Now,
1)9(9-8x)=2x+3
81-72x=2x+3
74x=78
x=39/37

2)9(9-8x)=-(2x+3)
81-72x=-2x-3
70x=84
x=6/5

So, x would be either 39/37 or 6/5

8. MysteryDove12 says:

9|9-8x|=2x+3    divide both sides by 9

l 9 - 8x l  =  [2x + 3] / 9        we have two equations

9 - 8x  = [2x + 3] / 9          and      9 - 8x =  - [2x + 3] / 9

multiply both sides by 9

81 - 72x  = 2x + 3                         81 - 72x  = -2x - 3

get the x's on one side and constants on the other

78  = 74x                                    84  = 70x

divide by 74                            divide by 70

78/74 = x =  39/37                      84/70  = x = 6/5

9. emilymendes546 says:

81-72x = 2x + 3

-74x = -84

x = 84/74= 42/37

-81 + 72x = 2x + 3

70x = 84

x = 84/70= 42/35= 6/5

10. ryleerose255 says:

12

expolntion:

12

=-11

13=12