solve for x : 9.8x - 13.8 = 2.7 - (1/5)x
Answers
Answer:
..x=
20
33
=1.650
Step-by-step explanation:
:
1
Simplify —
5
Equation at the end of step
1
:
98 138 27 1
((——•x)-———)-(——-(—•x)) = 0
10 10 10 5
STEP
2
:
27
Simplify ——
10
Equation at the end of step
2
:
98 138 27 x
((——•x)-———)-(——-—) = 0
10 10 10 5
STEP
3
:
Calculating the Least Common Multiple
3.1 Find the Least Common Multiple
The left denominator is : 10
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 1 1 1
Product of all
Prime Factors 10 5 10
Least Common Multiple:
10
Calculating Multipliers :
3.2 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 :
3.3 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
—————————————————— = ——
L.C.M 10
R. Mult. • R. Num. x • 2
—————————————————— = —————
L.C.M 10
Adding fractions that have a common denominator :
3.4 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 - (x • 2) 27 - 2x
———————————— = ———————
10 10
Equation at the end of step
3
:
98 138 (27 - 2x)
((—— • x) - ———) - ————————— = 0
10 10 10
STEP
4
:
69
Simplify ——
5
Equation at the end of step
4
:
98 69 (27 - 2x)
((—— • x) - ——) - ————————— = 0
10 5 10
STEP
5
:
49
Simplify ——
5
Equation at the end of step
5
:
49 69 (27 - 2x)
((—— • x) - ——) - ————————— = 0
5 5 10
STEP
6
:
Adding fractions which have a common denominator
6.1 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:
49x - (69) 49x - 69
—————————— = ————————
5 5
Equation at the end of step
6
:
(49x - 69) (27 - 2x)
—————————— - ————————— = 0
5 10
STEP
7
:
Calculating the Least Common Multiple
7.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 10
Number of times each prime factor
appears in the factorization of:
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