Answer: x=2.
Step-by-step explanation: a. \displaystyle |6x+4|=8∣6x+4∣=8
Write two equations and solve each:
6
x
+
4
=
8
6
x
+
4
=
−
8
6
x
=
4
6
x
=
−
12
x
=
2
3
x
=
−
2
The two solutions are \displaystyle x=\frac{2}{3}x=
3
2
, \displaystyle x=-2x=−2.
b. \displaystyle |3x+4|=-9∣3x+4∣=−9
There is no solution as an absolute value cannot be negative.
c. \displaystyle |3x - 5|-4=6∣3x−5∣−4=6
Isolate the absolute value expression and then write two equations.
|
3
x
−
5
|
−
4
=
6
|
3
x
−
5
|
=
10
3
x
−
5
=
10
3
x
−
5
=
−
10
3
x
=
15
3
x
=
−
5
x
=
5
x
=
−
5
3
There are two solutions: \displaystyle x=5x=5, \displaystyle x=-\frac{5}{3}x=−
3
5
.
d. \displaystyle |-5x+10|=0∣−5x+10∣=0
The equation is set equal to zero, so we have to write only one equation.
−
5
x
+
10
=
0
−
5
x
=
−
10
x
=
2
There is one solution: \displaystyle x=2x=2. Was this a lot of info for you.