Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "15.8" was replaced by "(158/10)". 2 more similar replacement(s)
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
x-(55/10)-((158/10)-2*x)>0
Step by step solution :
Step 1 :
79
Simplify ——
5
Equation at the end of step 1 :
55 79
(x - ——) - (—— - 2x) > 0
10 5
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
2x 2x • 5
2x = —— = ——————
1 5
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 :
2.2 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:
79 - (2x • 5) 79 - 10x
————————————— = ————————
5 5
Equation at the end of step 2 :
55 (79 - 10x)
(x - ——) - —————————— > 0
10 5
Step 3 :
11
Simplify ——
2
Equation at the end of step 3 :
11 (79 - 10x)
(x - ——) - —————————— > 0
2 5
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
x x • 2
x = — = —————
1 2
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
x • 2 - (11) 2x - 11
———————————— = ———————
2 2
Equation at the end of step 4 :
(2x - 11) (79 - 10x)
————————— - —————————— > 0
2 5
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 0 | 1 | 1 |
| Product of all Prime Factors | 2 | 5 | 10 |
Least Common Multiple:
10
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 = 5
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 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-11) • 5 —————————————————— = ——————————— L.C.M 10 R. Mult. • R. Num. (79-10x) • 2 —————————————————— = ———————————— L.C.M 10
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(2x-11) • 5 - ((79-10x) • 2) 30x - 213
———————————————————————————— = —————————
10 10
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
30x - 213 = 3 • (10x - 71)
Equation at the end of step 6 :
3 • (10x - 71)
—————————————— > 0
10
Step 7 :
7.1 Multiply both sides by 10
7.2 Divide both sides by 3
7.3 Divide both sides by 10
x-(71/10) > 0
Solve Basic Inequality :
7.4 Add 71/10 to both sides
x > 71/10
Inequality Plot :
7.5 Inequality plot for
3.000 X - 21.300 > 0
One solution was found :
x > 71/10How did we do?
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