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 :
8/15*x-17/30-(7/10)<0
Step by step solution :
Step 1 :
7
Simplify ——
10
Equation at the end of step 1 :
8 17 7
((—— • x) - ——) - —— < 0
15 30 10
Step 2 :
17
Simplify ——
30
Equation at the end of step 2 :
8 17 7
((—— • x) - ——) - —— < 0
15 30 10
Step 3 :
8
Simplify ——
15
Equation at the end of step 3 :
8 17 7
((—— • x) - ——) - —— < 0
15 30 10
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 15
The right denominator is : 30
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 1 | 1 | 1 |
| 5 | 1 | 1 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 15 | 30 | 30 |
Least Common Multiple:
30
Calculating Multipliers :
4.2 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 = 2
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
4.3 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. 8x • 2 —————————————————— = —————— L.C.M 30 R. Mult. • R. Num. 17 —————————————————— = —— L.C.M 30
Adding fractions that have a common denominator :
4.4 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:
8x • 2 - (17) 16x - 17
————————————— = ————————
30 30
Equation at the end of step 4 :
(16x - 17) 7
—————————— - —— < 0
30 10
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 30
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 1 | 1 |
| 3 | 1 | 0 | 1 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 30 | 10 | 30 |
Least Common Multiple:
30
Calculating Multipliers :
5.2 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 = 3
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (16x-17) —————————————————— = ———————— L.C.M 30 R. Mult. • R. Num. 7 • 3 —————————————————— = ————— L.C.M 30
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(16x-17) - (7 • 3) 16x - 38
—————————————————— = ————————
30 30
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
16x - 38 = 2 • (8x - 19)
Equation at the end of step 6 :
2 • (8x - 19)
————————————— < 0
30
Step 7 :
7.1 Multiply both sides by 30
7.2 Divide both sides by 2
7.3 Divide both sides by 8
x-(19/8) < 0
Solve Basic Inequality :
7.4 Add 19/8 to both sides
x < 19/8
Inequality Plot :
7.5 Inequality plot for
0.533 X - 1.267 < 0
One solution was found :
x < 19/8How did we do?
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