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): "0.6" was replaced by "(6/10)". 3 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 :
(156/10)-((27/10)*(z-1)-(6/10))<0
Step by step solution :
Step 1 :
3
Simplify —
5
Equation at the end of step 1 :
156 27 3
——— - ((—— • (z - 1)) - —) < 0
10 10 5
Step 2 :
27
Simplify ——
10
Equation at the end of step 2 :
156 27 3
——— - ((—— • (z - 1)) - —) < 0
10 10 5
Step 3 :
Equation at the end of step 3 :
156 27 • (z - 1) 3
——— - (———————————— - —) < 0
10 10 5
Step 4 :
Calculating the Least Common Multiple :
4.1 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 :
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 = 1
Right_M = L.C.M / R_Deno = 2
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. 27 • (z-1) —————————————————— = —————————— L.C.M 10 R. Mult. • R. Num. 3 • 2 —————————————————— = ————— L.C.M 10
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:
27 • (z-1) - (3 • 2) 27z - 33
———————————————————— = ————————
10 10
Equation at the end of step 4 :
156 (27z - 33)
——— - —————————— < 0
10 10
Step 5 :
78
Simplify ——
5
Equation at the end of step 5 :
78 (27z - 33)
—— - —————————— < 0
5 10
Step 6 :
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
27z - 33 = 3 • (9z - 11)
Calculating the Least Common Multiple :
7.2 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 1 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 10 | 10 |
Least Common Multiple:
10
Calculating Multipliers :
7.3 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 = 2
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
7.4 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 78 • 2 —————————————————— = —————— L.C.M 10 R. Mult. • R. Num. 3 • (9z-11) —————————————————— = ——————————— L.C.M 10
Adding fractions that have a common denominator :
7.5 Adding up the two equivalent fractions
78 • 2 - (3 • (9z-11)) 189 - 27z
—————————————————————— = —————————
10 10
Step 8 :
Pulling out like terms :
8.1 Pull out like factors :
189 - 27z = -27 • (z - 7)
Equation at the end of step 8 :
-27 • (z - 7)
————————————— < 0
10
Step 9 :
9.1 Multiply both sides by 10
9.2 Divide both sides by -27
Remember to flip the inequality sign:
Solve Basic Inequality :
9.3 Add 7 to both sides
z > 7
Inequality Plot :
9.4 Inequality plot for
-2.700 X + 18.900 > 0
One solution was found :
z > 7How did we do?
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