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): "34.5" was replaced by "(345/10)". 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-(39/10)-(-(345/10)+5*x)<0
Step by step solution :
Step 1 :
69
Simplify ——
2
Equation at the end of step 1 :
39 69
(-x - ——) - ((0 - ——) + 5x) < 0
10 2
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 2 as the denominator :
5x 5x • 2
5x = —— = ——————
1 2
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:
-69 + 5x • 2 10x - 69
———————————— = ————————
2 2
Equation at the end of step 2 :
39 (10x - 69)
(-x - ——) - —————————— < 0
10 2
Step 3 :
39
Simplify ——
10
Equation at the end of step 3 :
39 (10x - 69)
(-x - ——) - —————————— < 0
10 2
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 :
-x -x • 10
-x = —— = ———————
1 10
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
-x • 10 - (39) -10x - 39
—————————————— = —————————
10 10
Equation at the end of step 4 :
(-10x - 39) (10x - 69)
——————————— - —————————— < 0
10 2
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-10x - 39 = -1 • (10x + 39)
Calculating the Least Common Multiple :
6.2 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 1 | 1 |
| 5 | 1 | 0 | 1 |
| Product of all Prime Factors | 10 | 2 | 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 = 5
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. (-10x-39) —————————————————— = ————————— L.C.M 10 R. Mult. • R. Num. (10x-69) • 5 —————————————————— = ———————————— L.C.M 10
Adding fractions that have a common denominator :
6.5 Adding up the two equivalent fractions
(-10x-39) - ((10x-69) • 5) 306 - 60x
—————————————————————————— = —————————
10 10
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
306 - 60x = -6 • (10x - 51)
Equation at the end of step 7 :
-6 • (10x - 51)
——————————————— < 0
10
Step 8 :
8.1 Multiply both sides by 10
8.2 Divide both sides by -6
Remember to flip the inequality sign:
8.3 Divide both sides by 10
x-(51/10) > 0
Solve Basic Inequality :
8.4 Add 51/10 to both sides
x > 51/10
Inequality Plot :
8.5 Inequality plot for
-6.000 X + 30.600 > 0
One solution was found :
x > 51/10How did we do?
Please leave us feedback.