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 :
1/4*x+11/28-(23/14)>0
Step by step solution :
Step 1 :
23
Simplify ——
14
Equation at the end of step 1 :
1 11 23
((— • x) + ——) - —— > 0
4 28 14
Step 2 :
11
Simplify ——
28
Equation at the end of step 2 :
1 11 23
((— • x) + ——) - —— > 0
4 28 14
Step 3 :
1
Simplify —
4
Equation at the end of step 3 :
1 11 23
((— • x) + ——) - —— > 0
4 28 14
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 4
The right denominator is : 28
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 7 | 0 | 1 | 1 |
| Product of all Prime Factors | 4 | 28 | 28 |
Least Common Multiple:
28
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 = 7
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. x • 7 —————————————————— = ————— L.C.M 28 R. Mult. • R. Num. 11 —————————————————— = —— L.C.M 28
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:
x • 7 + 11 7x + 11
—————————— = ———————
28 28
Equation at the end of step 4 :
(7x + 11) 23
————————— - —— > 0
28 14
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 28
The right denominator is : 14
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 7 | 1 | 1 | 1 |
| Product of all Prime Factors | 28 | 14 | 28 |
Least Common Multiple:
28
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 = 2
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (7x+11) —————————————————— = ——————— L.C.M 28 R. Mult. • R. Num. 23 • 2 —————————————————— = —————— L.C.M 28
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(7x+11) - (23 • 2) 7x - 35
—————————————————— = ———————
28 28
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
7x - 35 = 7 • (x - 5)
Equation at the end of step 6 :
7 • (x - 5)
——————————— > 0
28
Step 7 :
7.1 Multiply both sides by 28
7.2 Divide both sides by 7
Solve Basic Inequality :
7.3 Add 5 to both sides
x > 5
Inequality Plot :
7.4 Inequality plot for
0.250 X - 1.250 > 0
One solution was found :
x > 5How did we do?
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