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 :
7/10-(4/5+g)>0
Step by step solution :
Step 1 :
4
Simplify —
5
Equation at the end of step 1 :
7 4
—— - (— + g) > 0
10 5
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 5 as the denominator :
g g • 5
g = — = —————
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:
4 + g • 5 5g + 4
————————— = ——————
5 5
Equation at the end of step 2 :
7 (5g + 4)
—— - ———————— > 0
10 5
Step 3 :
7
Simplify ——
10
Equation at the end of step 3 :
7 (5g + 4)
—— - ———————— > 0
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. 7 —————————————————— = —— L.C.M 10 R. Mult. • R. Num. (5g+4) • 2 —————————————————— = —————————— L.C.M 10
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
7 - ((5g+4) • 2) -10g - 1
———————————————— = ————————
10 10
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
-10g - 1 = -1 • (10g + 1)
Equation at the end of step 5 :
-10g - 1
———————— > 0
10
Step 6 :
6.1 Multiply both sides by 10
6.2 Multiply both sides by (-1)
Flip the inequality sign since you are multiplying by a negative number
10g+1 < 0
6.3 Divide both sides by 10
g+(1/10) < 0
Solve Basic Inequality :
6.4 Subtract 1/10 from both sides
g < -1/10
Inequality Plot :
6.5 Inequality plot for
-g - 0.100 > 0
One solution was found :
g < -1/10How did we do?
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