Step-by-step explanation:
One solution :
x = -1/12 = -0.083
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "1.2" was replaced by "(12/10)". 4 more similar replacement(s)
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(2/10)*(x-1)-(32/10)*x-((5/10)*(6*x+3)-(12/10))=0
Step by step solution :
Step 1 :
6
Simplify —
5
Equation at the end of step 1 :
2 32 5 6
((——•(x-1))-(——•x))-((——•(6x+3))-—) = 0
10 10 10 5
Step 2 :
1
Simplify —
2
Equation at the end of step 2 :
2 32 1 6
((——•(x-1))-(——•x))-((—•(6x+3))-—) = 0
10 10 2 5
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
6x + 3 = 3 • (2x + 1)
Equation at the end of step 4 :
2 32 3•(2x+1) 6
((——•(x-1))-(——•x))-(————————-—) = 0
10 10 2 5
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 5
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 0 1
5 0 1 1
Product of all
Prime Factors 2 5 10
Least Common Multiple:
10
Calculating Multipliers :
5.2 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 = 2
Making Equivalent Fractions :
5.3 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. 3 • (2x+1) • 5
—————————————————— = ——————————————
L.C.M 10
R. Mult. • R. Num. 6 • 2
—————————————————— = —————
L.C.M 10
Adding fractions that have a common denominator :
5.4 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:
3 • (2x+1) • 5 - (6 • 2) 30x + 3
———————————————————————— = ———————
10 10
Equation at the end of step 5 :
2 32 (30x+3)
((——•(x-1))-(——•x))-——————— = 0
10 10 10
Step 6 :
16
Simplify ——
5
Equation at the end of step 6 :
2 16 (30x+3)
((——•(x-1))-(——•x))-——————— = 0
10 5 10
Step 7 :
1
Simplify —
5
Equation at the end of step 7 :
1 16x (30x + 3)
((— • (x - 1)) - ———) - ————————— = 0
5 5 10
Step 8 :
Equation at the end of step 8 :
(x - 1) 16x (30x + 3)
(——————— - ———) - ————————— = 0
5 5 10
Step 9 :
Adding fractions which have a common denominator :
9.1 Adding fractions which 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-1) - (16x) -15x - 1
————————————— = ————————
5 5
Equation at the end of step 9 :
(-15x - 1) (30x + 3)
—————————— - ————————— = 0
5 10
Step 10 :
Step 11 :
Pulling out like terms :
11.1 Pull out like factors :
-15x - 1 = -1 • (15x + 1)
Step 12 :
Pulling out like terms :
12.1 Pull out like factors :
30x + 3 = 3 • (10x + 1)
