Answer: x > 69/25
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "5.06" was replaced by "(506/100)". 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+(23/10)-((506/100))>0
Step by step solution :
Step 1 :
253
Simplify ———
50
Equation at the end of step 1 :
23 253
(x + ——) - ——— > 0
10 50
Step 2 :
23
Simplify ——
10
Equation at the end of step 2 :
23 253
(x + ——) - ——— > 0
10 50
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 10 as the denominator :
x x • 10
x = — = ——————
1 10
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 • 10 + 23 10x + 23
——————————— = ————————
10 10
Equation at the end of step 3 :
(10x + 23) 253
—————————— - ——— > 0
10 50
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 50
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 1 1
5 1 2 2
Product of all
Prime Factors 10 50 50
Least Common Multiple:
50
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 = 5
Right_M = L.C.M / R_Deno = 1
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. (10x+23) • 5
—————————————————— = ————————————
L.C.M 50
R. Mult. • R. Num. 253
—————————————————— = ———
L.C.M 50
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(10x+23) • 5 - (253) 50x - 138
———————————————————— = —————————
50 50
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
50x - 138 = 2 • (25x - 69)
Equation at the end of step 5 :
2 • (25x - 69)
—————————————— > 0
50
Step 6 :
6.1 Multiply both sides by 50
6.2 Divide both sides by 2
6.3 Divide both sides by 25
x-(69/25) > 0
