X-(2x+8/3)=1/4(x-(2-x)/6)-3
Answers
Answer:x = 148/29 = 5.103
Step-by-step explanation:
x-2*x+8/3-(1/4*(x-2-x/6)-3)=0
Step by step solution :
Step 1 :
x
Simplify —
6
Equation at the end of step 1 :
8 1 x
(-x+—)-((—•((x-2)-—))-3) = 0
3 4 6
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 6 as the denominator :
x-2*x+8/3-(1/4*(x-2-x/6)-3)=0
Step by step solution :
Step 1 :
x
Simplify —
6
Equation at the end of step 1 :
8 1 x
(-x+—)-((—•((x-2)-—))-3) = 0
3 4 6
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 6 as the denominator :
x-2*x+8/3-(1/4*(x-2-x/6)-3)=0
Step by step solution :
Step 1 :
x
Simplify —
6
Equation at the end of step 1 :
8 1 x
(-x+—)-((—•((x-2)-—))-3) = 0
3 4 6
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 6 as the denominator :
x - 2 (x - 2) • 6
x - 2 = ————— = ———————————
1 6
Equation at the end of step 2 :
8 1 (5x-12)
(-x+—)-((—•———————)-3) = 0
3 4 6
Step 3 :
1
Simplify —
4
Equation at the end of step 3 :
8 1 (5x - 12)
(-x + —) - ((— • —————————) - 3) = 0
3 4 6
Step 4 :
Equation at the end of step 4 :
8 (5x - 12)
(-x + —) - (————————— - 3) = 0
3 24
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 24 as the denominator :
3 3 • 24
3 = — = ——————
1 24
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
(5x-12) - (3 • 24) 5x - 84
—————————————————— = ———————
24 24
Equation at the end of step 5 :
8 (5x - 84)
(-x + —) - ————————— = 0
3 24
Step 6 :
8
Simplify —
3
Equation at the end of step 6 :
8 (5x - 84)
(-x + —) - ————————— = 0
3 24
Step 7 :
Rewriting the whole as an Equivalent Fraction :
7.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
-x -x • 3
-x = —— = ——————
1 3
Adding fractions that have a common denominator :
7.2 Adding up the two equivalent fractions
-x • 3 + 8 8 - 3x
—————————— = ——————
3 3
Equation at the end of step 7 :
(8 - 3x) (5x - 84)
———————— - ————————— = 0
3 24
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 24
Number of times each prime factor
appears in the factorization of:
Least Common Multiple:
24
Calculating Multipliers :
8.2 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 = 8
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
8.3 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. (8-3x) • 8
—————————————————— = ——————————
L.C.M 24
R. Mult. • R. Num. (5x-84)
—————————————————— = ———————
L.C.M 24
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
(8-3x) • 8 - ((5x-84)) 148 - 29x
—————————————————————— = —————————
24 24
Equation at the end of step 8 :
148 - 29x
————————— = 0
24
Step 9 :
When a fraction equals zero :
9.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
148-29x
——————— • 24 = 0 • 24
24
Now, on the left hand side, the 24 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
148-29x = 0
Solving a Single Variable Equation :
9.2 Solve : -29x+148 = 0
Subtract 148 from both sides of the equation :
-29x = -148
Multiply both sides of the equation by (-1) : 29x = 148
Divide both sides of the equation by 29:
x = 148/29 = 5.103
One solution was found :
x = 148/29 = 5.103