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
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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