Answer:
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
