Mathematics, 13.10.2019 03:20 bbysl15

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

Answers: 3

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Answers

x = 6/5 ; or, write as: "1 1/5" ; or,write as: "1.2" ;

x =  39/37 = 1 2/37 = 1.0540540540540541 .

Explanation:

Given:

9|9−8x|=2x+3 ; Solve for "x" ;

DIvide EACH side of the equation by "9" ;

{ 9|9−8x| } / 9 = { 2x + 3 } / 9 ;

to get:

|9−8x| = (2x + 3) / 9 ;

Given the "absolute value" on the left-hand side; we have
"Case 1" and "Case 2" scenarios:

Case 1:

9 − 8x = (2x+ 3) / 9 ;

↔ -8x + 9 = (2x+ 3) / 9 ;

Case 2:

- (9 − 8x) = -9 + 8x = 8x − 9 ;

↔ 8x − 9 = (2x + 3) / 9

Let us start with "Case 1" :

-8x + 9 = (2x + 3) / 9 ;

→ 9*(-8x + 9) = 2x + 3 ;

→ -72x + 81 = 2x + 3 ;

  → Subtract "81" ; and "2x" from EACH side of the equation ;

→ -72x + 81 − 81 − 2x = 2x + 3 − 81 − 2x ;

to get: -74x = -78 ;

Divide EACH side of the equation by "-74" ; to isolate "x" on one side of the equation; and to solve for "x" ;

-74x / -74 = -78/-74 ;

x = 78/74 = 39/37 = 1 2/37 ; or, 1.0540540540540541 .

Now, let's continue with: "Case 2" :

8x − 9 = (2x + 3) / 9 ;

→ 9*(8x − 9) = 2x + 3 ;

→ 72x − 81 = 2x + 3 ;

Subtract "2x" ; and add "81" ; to BOTH sides of the equation:

→ 72x − 81 − 2x + 81 = 2x + 3 − 2x + 81 ;

to get: → 70x = 84 ;

Divide EACH side of the equation by "70" ; to isolate "x" on one side of the equation; and to solve for "x" ;

  → 70x / 70 = 84 / 70 ;

  → x = 6/5 = 1 1/5 = 1.2

Answer from: jeremiahsingleton

³⁹/₃₇ and ⁶/₅

Further explanation

For any real number x, the absolute value of x is denoted by | x | and

$\boxed{ \ |x| = \left \{ {{x, \ x \geq 0 } \atop {-x, \ x < 0}} \right. \ }$

Our case is given by:

$\boxed{ \ 9|9 - 8x| = 2x + 3 \ }$

Part-1

$\boxed{ \ 9(9 - 8x) = 2x + 3 \ }$

$\boxed{ \ 81 - 72x = 2x + 3 \ }$

$\boxed{ \ - 2x - 72x = 3 - 81 \ }$

$\boxed{ \ - 74x = - 78 \ }$

$\boxed{ \ x = \frac{-78}{-74} \rightarrow \frac{divided \ by \ (-2)}{divided \ by \ (-2)} \rightarrow \boxed{ \ x = \frac{39}{37} \ } \ }$

Part-2

$\boxed{ \ - 9(9 - 8x) = 2x + 3 \ }$

$\boxed{ \ - 81 + 72x = 2x + 3 \ }$

$\boxed{ \ 72x - 2x = 3 + 81 \ }$

$\boxed{ \ 70x = 84 \ }$

$\boxed{ \ x = \frac{84}{70} \rightarrow \frac{divided \ by \ 14}{divided \ by \ 14} \rightarrow \boxed{ \ x = \frac{6}{5} \ } \ }$

Thus, the solution is $\boxed{ \ x = \frac{39}{37} \ or \ x = \frac{6}{5}. \ }$

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Keywords: solve the equation, the absolute value, check for extraneous solutions, 9|9 - 8x| = 2x + 3, the solution

Answer from: Quest

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

Point z is equidistant from the sides of δrst. which must be true? ctzaszaszzsb

Answer from: Quest

step-by-step explanation:

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