Mathematics, 13.10.2019 03:20 bbysl15

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

Answers: 3

Show answers

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 $\boxed{ \ x = \frac{39}{37} \ or \ x = \frac{6}{5}. \ }$

Learn moreA linear programming problem link Does Marcus pay tax? linkAbout complex numbers link

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

Answer from: Quest

investment b is an ordinary annuity with $3,909.64 in the account after one year.

step-by-step explanation:

Answer from: Quest

Ihonestly don’t no that

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 14:50, gshreya2005

(a) compute the maclaurin polynomial m2(x) for f(x) = cos x. (b) use the polynomial of part (a) to estimate cos π 12. (c) use a calculator to compute the error made using the estimate from part (b) for the value of cos π 12. remember that the error is defined to be the absolute value of the difference between the true value and the estimate.

Answers: 2

continue

Mathematics, 21.06.2019 16:30, shanua

What is the difference between regular convex and concave polygons

Answers: 1

continue

Mathematics, 21.06.2019 17:20, organicmemez

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. they randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. which statistical analysis should be performed to answer the researchers' question?

Answers: 2

continue

Mathematics, 21.06.2019 22:00, anastasiakonni1

Jayne is studying urban planning and finds that her town is decreasing in population by 3% each year. the population of her town is changing by a constant rate. true or false?

Answers: 3

continue

You know the right answer?

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