find the root of the following equations
3x-1/3=2/3
Answers
Answer:
Step 1 :
2
Simplify —
3
Equation at the end of step 1 :
2 1 2
((— • x) - —) - — = 0
3 3 3
Step 2 :
1
Simplify —
3
Equation at the end of step 2 :
2 1 2
((— • x) - —) - — = 0
3 3 3
Step 3 :
2
Simplify —
3
Equation at the end of step 3 :
2 1 2
((— • x) - —) - — = 0
3 3 3
Step 4 :
Adding fractions which have a common denominator :
4.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x - (1) 2x - 1
———————— = ——————
3 3
Equation at the end of step 4 :
(2x - 1) 2
———————— - — = 0
3 3
Step 5 :
Adding fractions which have a common denominator :
5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(2x-1) - (2) 2x - 3
———————————— = ——————
3 3
Equation at the end of step 5 :
2x - 3
—————— = 0
3
Step 6 :
When a fraction equals zero :
6.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
2x-3
———— • 3 = 0 • 3
3
Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
2x-3 = 0
Solving a Single Variable Equation :
6.2 Solve : 2x-3 = 0
Add 3 to both sides of the equation :
2x = 3
Divide both sides of the equation by 2:
x = 3/2 = 1.500
One solution was found :
x = 3/2 = 1.500
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3x-1/3=2/3
3x=2/3+1/3
3x=2+1/3
3x=3/3
3x=1
X=1/3