SOLUTION: I have two absolute question. The first is 3|6-d|=18 and the other one is 1/4|6x-3|=18.75

Question 849516: I have two absolute question. The first is 3|6-d|=18 and the other one is
1/4|6x-3|=18.75
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
first problem:

3|6-d| = 18

divide both sides of this equation by 3 to get:

|6-d| = 6

break this up into 2 equations as follows:

first equation is (6-d) = 6

second equation is (6-d) = -6

first equation is solved as follows:

6-d = 6
subtract 6 from both sides of this equation to get:

-d = 0

multiply both sides of this equation by -2 to get:

d = 0

second equation is solved as follows:

(6-d) = -6

subtract 6 from both sides of this equation to get:

-d = -12

multiply both sidesof this equation by -1 to get:

d = 12

your solutions are that d is either equal to 0 or d is equal to 12.

confirm by substituting in the original equation.

3 * |6-d| = 18 is the original equation.

replace d with 0 to get 3 * |6-0| = 18 which simplifies to:

18 = 18, confirming d = 0 is good.

replace d with 12 to get 3 * |6 - 12| = 18 which simplifies to:

3 * |-6| = 18 which becomse 18 = 18 because the absolute value of -6 is equal to 6.

both solutions are confirmed to be true.

second problem:

1/4 * |6x-3| = 18.75

multiply both sides of this equation by 4 and you get:

|6x-3| = 75

break this up into 2 equations:

first equation is (6x-3) = 75

second equation is (6x-3) = -75

solve each equation for x.

first equation is solved as follows:
6x-3 = 75
add 3 to both sides to get:
6x = 78
divide both sides by 6 to get:
x = 13

second equation is solved as follows:
6x-3 = -75
add 3 to both sides to get:
6x = -72
divide both sides by 6 to get:
x = -12

x is either 13 or -12

when x is 13, 1/4 * |6x-3| is equal to 1/4 * |75| which is equal to 18.75.

when x is -12, 1/4 * |6x-3| is equal to 1/4 * |-75| which is equal to 18.75.

this is because the absolute value of a number is always positive.

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