[absolutevalue equations][section 31]
(1.) |a + 3| = 2 here is the problem
a + 3 = 2 a + 3 = -2 set = to 2 and to -2
-3 -3
-3 -3 subtract 3 fr ea side
____________ _______________
a = -1 ,
x = -5 subtract
result: a = -1, a = -5
(2.) |3x - 6| = 12 here is the problem
3x - 6 = 12 3x - 6 = -12
set = to 12 & to -12
+6 +6
+6 +6 add 6 to each side
_______________ ________________
3x =
18 , 3x =
-6 add
___ ___
____ ____
3 3 3 3
divide ea side by 3
x = 6 , x =
-2 divide and cancel
result: x = 6 , x =
-2
(3.) |t + 1| = 9 here is the problem
t + 1 = 9 t + 1 = -9 set = to 9 and to -9
-1 -1
-1 -1 subtract 1 from each side
___________ _____________
t = 8 ,
t = -10 subtract
result: t = 8 , t =
-10
(4.) |6k + 6| = 24 here is the problem
6k + 6 = 24 6k + 6 = -24 set equal to 24 & to -24
-6 -6
-6 -6 subtract 6 from each side
_____________ _________________
6k
= 18 ,
6k = -30
subtract
___ ___
___ ______
6 6 6 6
divide ea side by 6
k = 3 ,
k = -5 divide and
cancel
result: k = 3 , k =
-5
(5.) |3m + 2| = 17 here is the problem
3m + 2 = 17 3m + 2 = -17 set equal to 17 & to -17
-2 -2
-2 -2 subtract 2 from each side
_____________ _______________
3m
= 15 ,
3m = -19
subtract
___
___ ___ ____
3 3
3 3 divide each side by 3
m = 5 ,
m = -6 1/3 divide and
cancel
result: m = 5 , m
= -6 1/3
(6.) |6r + 2| = 10 here is the problem
6r + 2 = 10 6r + 2 = -10 set equal to 10 and to -10
-2
-2 -2 -2
subtract 2 from each side
______________ _______________
6r
= 8 6r = -12
subtract
__
___ ___ _____
6
6 6 6
divide each side by 6
r = 1 1/3 r = -2 divide and cancel
result: r = 1 1/3 , r
= -2
(7.) |3(t - 1)| - 4 = 16 here is the problem
|3t - 3| - 4 = 16 multiply thru parentheses
+4 +4
add 4 to each side
__________________
|3t - 3| =
20 add
3t - 3 = 20 3t - 3 = -20 set equal to 20 and to -20
+
3 +3 +3
+3 add 3 to each side
______________ ______________
3t
= 23 , 3t
= -17 add
__
___ ___ _____
3 3
3 3 divide each side by 3
t = 7 2/3 t = -5 2/3 divide and cancel
result: t = 7 2/3 , t =
-5 2/3
(8.) |7x - 5| = 30 here is the problem
7x - 5 = 30 7x - 5 = -30 set equal to 30 & to -30
+ 5 +5
+5 +5 add 5 to each side
_______________ ____________
7x
= 35 , 7x =
-25 add
___ ___
__ ____
7 7
7 7 divide each side by 7
x = 5 ,
x = -3 4/7 divide and
cancel
result: x = 5 , x =
-3 4/7
(9.) |8 - 2(y - 1)| + 5 = 9 here is the problem
|8 - 2y + 2| + 5 = 9 multiply thru parentheses
|10 - 2y| + 5 = 9 combine like terms
-5 -5
subtract 5 from each side
______________________
|10 - 2y|
= 4 subtract
10 - 2y = 4 10 - 2y = -4 set equal to 4 & to -4
-10 + 2y = -4 -10 + 2y = 4 multiply thru by -1
+ 10
+ 10 +10 +10
add 10 to each side
______________ ________________
2y = 6 , 2y = 14 add
___ ___ ___
____
2 2
2 2 divide each side by 2
y = 3 , y
= 7 divide and cancel
result: y = 3 , y
= 7
(10.) 12 = |3 - x| here is the problem
3 - x = 12 3 - x = -12 set equal to 12 and to -12
-3 + x = -12 -3 + x = 12 multiply thru by -1
+
3 + 3
+ 3 + 3 add 3 to each side
__________________ _______________
x = -9
, x = 15 add
result: x = -9 , x =
15