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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d = sqrt((x2-x1)^2+(y2-y1)^2)

d = sqrt((-2-(-10))^2+(2-2)^2)

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For the points (-3,-1) and (5,1), the distance is...

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d = sqrt((5-(-3))^2+(1-(-1))^2)

d = sqrt((5+3)^2+(1+1)^2)

d = sqrt((8)^2+(2)^2)

d = sqrt(64+4)

d = sqrt(68)

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For the points (-3,-2) and (1,3), the distance is...

d = sqrt((x2-x1)^2+(y2-y1)^2)

d = sqrt((1-(-3))^2+(3-(-2))^2)

d = sqrt((1+3)^2+(3+2)^2)

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For the points (-3,-5) and (-2,-4), the distance is...

d = sqrt((x2-x1)^2+(y2-y1)^2)

d = sqrt((-2-(-3))^2+(-4-(-5))^2)

d = sqrt((-2+3)^2+(-4+5)^2)

d = sqrt((1)^2+(1)^2)

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For the points (0,0) and (5,5), the distance is...

d = sqrt((x2-x1)^2+(y2-y1)^2)

d = sqrt((5-0)^2+(5-0)^2)

d = sqrt((5)^2+(5)^2)

d = sqrt(25+25)

d = sqrt(50)

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For the points (1,2) and (1,-10), the distance is...

d = sqrt((x2-x1)^2+(y2-y1)^2)

d = sqrt((1-1)^2+(-10-2)^2)

d = sqrt((0)^2+(-12)^2)

d = sqrt(0+144)

d = sqrt(144)

d = 12

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For the points (1,2) and (5,2), the distance is...

d = sqrt((x2-x1)^2+(y2-y1)^2)

d = sqrt((5-1)^2+(2-2)^2)

d = sqrt((4)^2+(0)^2)

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For the points (2,3) and (10,9), the distance is...

d = sqrt((x2-x1)^2+(y2-y1)^2)

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See the attached image for how the answers match up (take note of the letter labels)