7 ∣x−2∣+7=−2∣x−2∣ +2

 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.