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 :
x/3+7-(51/2)>0
Step by step solution :
Step 1 :
51
Simplify ——
2
Equation at the end of step 1 :
x 51
(— + 7) - —— > 0
3 2
Step 2 :
x
Simplify —
3
Equation at the end of step 2 :
x 51
(— + 7) - —— > 0
3 2
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 3 as the denominator :
7 7 • 3
7 = — = —————
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 :
3.2 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 + 7 • 3 x + 21
————————— = ——————
3 3
Equation at the end of step 3 :
(x + 21) 51
———————— - —— > 0
3 2
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 1 | 0 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 3 | 2 | 6 |
Least Common Multiple:
6
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 = 3
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+21) • 2 —————————————————— = —————————— L.C.M 6 R. Mult. • R. Num. 51 • 3 —————————————————— = —————— L.C.M 6
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(x+21) • 2 - (51 • 3) 2x - 111
————————————————————— = ————————
6 6
Equation at the end of step 4 :
2x - 111
———————— > 0
6
Step 5 :
5.1 Multiply both sides by 6
5.2 Divide both sides by 2
x-(111/2) > 0
Solve Basic Inequality :
5.3 Add 111/2 to both sides
x > 111/2
Inequality Plot :
5.4 Inequality plot for
0.333 x - 18.500 > 0
One solution was found :
x > 111/2How did we do?
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