HELP FAST 2/3x-1/5>1
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Answer:
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Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
2/3*x-1/5-(1)>0
Step by step solution :
STEP1:
1 Simplify — 5
Equation at the end of step1:
2 1 ((— • x) - —) - 1 > 0 3 5
STEP2:
2 Simplify — 3
Equation at the end of step2:
2 1 ((— • x) - —) - 1 > 0 3 5
STEP3:Calculating the Least Common Multiple
3.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 5
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 31015011 Product of all
Prime Factors 3515
Least Common Multiple:
15
Calculating Multipliers :
3.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5
Right_M = L.C.M / R_Deno = 3
Making Equivalent Fractions :
3.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 2x • 5 —————————————————— = —————— L.C.M 15 R. Mult. • R. Num. 3 —————————————————— = —— L.C.M 15
Adding fractions that have a common denominator :
3.4 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:
2x • 5 - (3) 10x - 3 ———————————— = ——————— 15 15
Equation at the end of step3:
(10x - 3) ————————— - 1 > 0 15
STEP4:Rewriting the whole as an Equivalent Fraction
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 15 as the denominator :
1 1 • 15 1 = — = —————— 1 15
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 :
4.2 Adding up the two equivalent fractions
(10x-3) - (15) 10x - 18 —————————————— = ———————— 15 15
STEP5:Pulling out like terms
5.1 Pull out like factors :
10x - 18 = 2 • (5x - 9)
Equation at the end of step5:
2 • (5x - 9) ———————————— > 0 15
STEP6:
6.1 Multiply both sides by 15
6.2 Divide both sides by 2
6.3 Divide both sides by 5
x-(9/5) > 0
Solve Basic Inequality :
6.4 Add 9/5 to both sides
x > 9/5
Inequality Plot :
6.5 Inequality plot for
0.667 X - 1.200 > 0
One solution was found :
x > 9/5
Answer:
Hope it helps
Step-by-step explanation:
2/3x -1/5 > 1
2x/3 > 1 + 1 / 5
2x/3 > 5+1/5
2x/3 > 6/5
x > 6/5 × 3/2
x > 9/5
Therefore x is greater than 9/5
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