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): "1.8" was replaced by "(18/10)". 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 :
4*x-(103/10)-(21*x-(18/10))<0
Step by step solution :
Step 1 :
9
Simplify —
5
Equation at the end of step 1 :
103 9
(4x - ———) - (21x - —) < 0
10 5
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 5 as the denominator :
21x 21x • 5
21x = ——— = ———————
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:
21x • 5 - (9) 105x - 9
————————————— = ————————
5 5
Equation at the end of step 2 :
103 (105x - 9)
(4x - ———) - —————————— < 0
10 5
Step 3 :
103
Simplify ———
10
Equation at the end of step 3 :
103 (105x - 9)
(4x - ———) - —————————— < 0
10 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 10 as the denominator :
4x 4x • 10
4x = —— = ———————
1 10
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
4x • 10 - (103) 40x - 103
——————————————— = —————————
10 10
Equation at the end of step 4 :
(40x - 103) (105x - 9)
——————————— - —————————— < 0
10 5
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
105x - 9 = 3 • (35x - 3)
Calculating the Least Common Multiple :
6.2 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 10 | 5 | 10 |
Least Common Multiple:
10
Calculating Multipliers :
6.3 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 :
6.4 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. (40x-103) —————————————————— = ————————— L.C.M 10 R. Mult. • R. Num. 3 • (35x-3) • 2 —————————————————— = ——————————————— L.C.M 10
Adding fractions that have a common denominator :
6.5 Adding up the two equivalent fractions
(40x-103) - (3 • (35x-3) • 2) -170x - 85
————————————————————————————— = ——————————
10 10
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
-170x - 85 = -85 • (2x + 1)
Equation at the end of step 7 :
-85 • (2x + 1)
—————————————— < 0
10
Step 8 :
8.1 Multiply both sides by 10
8.2 Divide both sides by -85
Remember to flip the inequality sign:
8.3 Divide both sides by 2
x+(1/2) > 0
Solve Basic Inequality :
8.4 Subtract 1/2 from both sides
x > -1/2
Inequality Plot :
8.5 Inequality plot for
-17.000 X - 8.500 > 0
One solution was found :
x > -1/2How did we do?
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