Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
2/5*x-8/3-(7/15*x+1/3)>0
Step by step solution :
Step 1 :
1
Simplify —
3
Equation at the end of step 1 :
2 8 7 1
((—•x)-—)-((——•x)+—) > 0
5 3 15 3
Step 2 :
7
Simplify ——
15
Equation at the end of step 2 :
2 8 7 1
((—•x)-—)-((——•x)+—) > 0
5 3 15 3
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 15
The right denominator is : 3
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 1 | 1 | 1 |
| 5 | 1 | 0 | 1 |
| Product of all Prime Factors | 15 | 3 | 15 |
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 = 1
Right_M = L.C.M / R_Deno = 5
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. 7x —————————————————— = —— L.C.M 15 R. Mult. • R. Num. 5 —————————————————— = —— 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:
7x + 5 7x + 5
—————— = ——————
15 15
Equation at the end of step 3 :
2 8 (7x + 5)
((— • x) - —) - ———————— > 0
5 3 15
Step 4 :
8
Simplify —
3
Equation at the end of step 4 :
2 8 (7x + 5)
((— • x) - —) - ———————— > 0
5 3 15
Step 5 :
2
Simplify —
5
Equation at the end of step 5 :
2 8 (7x + 5)
((— • x) - —) - ———————— > 0
5 3 15
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 3
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 0 | 1 |
| 3 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 3 | 15 |
Least Common Multiple:
15
Calculating Multipliers :
6.2 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 = 3
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 2x • 3 —————————————————— = —————— L.C.M 15 R. Mult. • R. Num. 8 • 5 —————————————————— = ————— L.C.M 15
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
2x • 3 - (8 • 5) 6x - 40
———————————————— = ———————
15 15
Equation at the end of step 6 :
(6x - 40) (7x + 5)
————————— - ———————— > 0
15 15
Step 7 :
Step 8 :
Pulling out like terms :
8.1 Pull out like factors :
6x - 40 = 2 • (3x - 20)
Adding fractions which have a common denominator :
8.2 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:
2 • (3x-20) - ((7x+5)) -x - 45
—————————————————————— = ———————
15 15
Step 9 :
Pulling out like terms :
9.1 Pull out like factors :
-x - 45 = -1 • (x + 45)
Equation at the end of step 9 :
-x - 45
——————— > 0
15
Step 10 :
10.1 Multiply both sides by 15
10.2 Multiply both sides by (-1)
Flip the inequality sign since you are multiplying by a negative number
x+45 < 0
Solve Basic Inequality :
10.3 Subtract 45 from both sides
x < -45
Inequality Plot :
10.4 Inequality plot for
-0.067 x - 3.000 > 0
One solution was found :
x < -45How did we do?
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