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Solve the equation. Check for extraneous solutions. 9 |9−8x|=2x+3 please show steps

1 Answer

4 votes

Answer:

x = 0.6 , x = 2

Explanation:

the absolute value function always gives a positive value, that is

| - a | = | a | = a

the expression inside the bars, however , can be positive or negative, so

9 - 8x = 2x +3 ( subtract 2x from both sides )

9 - 10x = 3 ( subtract 9 from both sides )

- 10x = - 6 ( divide both sides by - 10 )

x = 0.6

Or

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

- 9 + 8x = 2x + 3 ( subtract 2x from both sides )

- 9 + 6x = 3 (add 9 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

As a check

substitute these values into the equation and if both sides are equal then they are the solutions.

x = 0.6

left side = | 9 - 8(0.6) | = | 9 - 4.8 | = | 4.2 | = 4.2

right side = 2(0.6) + 3 = 1.2 + 3 = 4.2= left side

-------------------------------------------------------

x = 2

left side = | 9 - 8(2) | = | 9 - 16 | = | - 7 | = 7

right side = 2(2) + 3 = 4 + 3 = 7 = left side

the solutions to the equation are x = 0.6 and x = 2

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