Answer:1/3
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
3/2*(x-1/3)-(-5*x)>0
Step by step solution :
STEP
1
:
1
Simplify —
3
Equation at the end of step
1
:
3 1
(— • (x - —)) - -5x > 0
2 3
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 3 as the denominator :
x x • 3
x = — = —————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • 3 - (1) 3x - 1
——————————— = ——————
3 3
Equation at the end of step
2
:
3 (3x - 1)
(— • ————————) - -5x > 0
2 3
STEP
3
:
3
Simplify —
2
Equation at the end of step
3
:
3 (3x - 1)
(— • ————————) - -5x > 0
2 3
STEP
4
:
Equation at the end of step
4
:
(3x - 1)
———————— - -5x > 0
2
STEP
5
:
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 2 as the denominator :
-5x -5x • 2
-5x = ——— = ———————
1 2
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
(3x-1) - (-5x • 2) 13x - 1
—————————————————— = ———————
2 2
The equation at the end of step
5
:
13x - 1
——————— > 0
2
STEP
6
:
6.1 Multiply both sides by 2
6.2 Divide both sides by 13
x-(1/13) > 0
Solve Basic Inequality :
6.3 Add 1/13 to both sides
x > 1/13
