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3 years ago

2|x - 3| - 5 = 7 “solve the equation”

Mathematics

2 answers:

djverab [1.8K]3 years ago

7 0

Answer:

x = - 3, x = 9

Step-by-step explanation:

Given

2| x - 3 | - 5 = 7 ( add 5 to both sides )

2|x - 3 | = 12 ( divide both sides by 2 )

| x - 3 | = 6

The absolute value function always gives a positive value, however, the expression inside the bars can be positive or negative, that is

x - 3 = 6 or - (x - 3) = 6

Solving both equations

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

x = 9

- (x - 3) = 6

- x + 3 = 6 ( subtract 3 from both sides )

- x = 3 ( multiply both sides by - 1 )

x = - 3

As a check

2|9 - 3| - 5 = 2|6| - 5 = 12 - 5 = 7 ← Correct

2|- 3 - 3| - 5 = 2|- 6| - 5 = 2 |6| - 5 = 12 - 5 = 7 ← Correct

Thus the solutions are x = - 3, x = 9

nasty-shy [4]3 years ago

4 0

Answer:

Combine solutions: x=-3 or x=9

Step-by-step explanation:

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