|2 1/3 x+0.3|=3.5
|2 1/3 x-0.3|=3.5

1) x = 48/35, -57/35

2) x = -48/35, 57/35

Step-by-step explanation:

|2 1/3 x+0.3|=3.5

7/3x + 0.3 = 3.5

7/3x = 3.2

x = 48/35 or 1.37

7/3x + 0.3 = -3.5

7/3x = -3.8

x = -57/35 or -1.63

Answers:

x = 48/35, -57/35

|2 1/3 x-0.3|=3.5

7/3x - 0.3 = 3.5

7/3x = 3.8

x = 57/35 or 1.63

7/3x - 0.3 = -3.5

7/3x = -3.2

x = -48/35 or -1.37

Answers:

x = -48/35, 57/35

see below

Step-by-step explanation:

|2 1/3 x+  0.3|=3.5   and   |2 1/3 x-0.3|=3.5

We have two absolute value equations

Lets solve the first one first

|2 1/3 x+0.3|=3.5

To solve absolute values we get two sets of equations, one positive and one negative

2 1/3 x+0.3=3.5  and 2 1/3 x+0.3=-3.5

Subtract .3 from each side

2 1/3 x+0.3-.3=3.5-.3   and 2 1/3 x+0.3-.3 =-3.5-.3

2 1/3 x+=3.2   and 2 1/3 x =-3.8

We need to change the fraction to a mixed number

2 1/3 = (3*2+1) /3 = 7/3

7/3 x+=3.2   and 7/3 x =-3.8

Multiply each side by 3/7 to isolate x

3/7*7/3 x+=3.2 *3/7      and 3/7*7/3 x =-3.8*3/7

x = 1.371428571                      -1.628571429

Now we solve the second set of equations

|2 1/3 x-0.3|=3.5

To solve absolute values we get two sets of equations, one positive and one negative

2 1/3 x-0.3=3.5  and 2 1/3 x-0.3=-3.5

Add .3 from each side

2 1/3 x+0.3-.3=3.5+.3   and 2 1/3 x+0.3-.3 =-3.5+.3

2 1/3 x+=3.8   and 2 1/3 x =-3.2

We need to change the fraction to a mixed number

2 1/3 = (3*2+1) /3 = 7/3

7/3 x+=3.28  and 7/3 x =-3.2

Multiply each side by 3/7 to isolate x

3/7*7/3 x+=3.8 *3/7      and 3/7*7/3 x =-3.2*3/7

x = 1.628571429       x =-1.371428571

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answer:

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