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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