solve the following 1/2(-56x+4(2x-7) =(1-3x) -42
Answers
Answer:
Step by Step Solution

Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x-(5*x+1/7+3*x-5/2)=0
Step by step solution :
STEP1:
5 Simplify — 2
Equation at the end of step1:
1 5 2x - (((5x + —) + 3x) - —) = 0 7 2
STEP2:
1 Simplify — 7
Equation at the end of step2:
1 5 2x - (((5x + —) + 3x) - —) = 0 7 2
STEP3:Rewriting the whole as an Equivalent Fraction
3.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 7 as the denominator :
5x 5x • 7 5x = —— = —————— 1 7
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:
5x • 7 + 1 35x + 1 —————————— = ——————— 7 7
Equation at the end of step3:
(35x + 1) 5 2x - ((————————— + 3x) - —) = 0 7 2
STEP4:
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 7 as the denominator :
3x 3x • 7 3x = —— = —————— 1 7
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
(35x+1) + 3x • 7 56x + 1 ———————————————— = ——————— 7 7
Equation at the end of step4:
(56x + 1) 5 2x - (————————— - —) = 0 7 2
STEP5:
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 7
The right denominator is : 2
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 71012011 Product of all
Prime Factors 7214
Least Common Multiple:
14
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 = 2
Right_M = L.C.M / R_Deno = 7
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. (56x+1) • 2 —————————————————— = ——————————— L.C.M 14 R. Mult. • R. Num. 5 • 7 —————————————————— = ————— L.C.M 14
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(56x+1) • 2 - (5 • 7) 112x - 33 ————————————————————— = ————————— 14 14
Equation at the end of step5:
(112x - 33) 2x - ——————————— = 0 14
STEP6:
Rewriting the whole as an Equivalent Fraction :
6.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 14 as the denominator :
2x 2x • 14 2x = —— = ——————— 1 14
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions
2x • 14 - ((112x-33)) 33 - 84x ————————————————————— = ———————— 14 14
STEP7:
Pulling out like terms :
7.1 Pull out like factors :
33 - 84x = -3 • (28x - 11)
Equation at the end of step7:
-3 • (28x - 11) ——————————————— = 0 14
STEP8:
When a fraction equals zero :
8.1 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:
-3•(28x-11) ——————————— • 14 = 0 • 14 14
Now, on the left hand side, the 14 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-3 • (28x-11) = 0
Equations which are never true:
8.2 Solve : -3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
8.3 Solve : 28x-11 = 0
Add 11 to both sides of the equation :
28x = 11
Divide both sides of the equation by 28:
x = 11/28 = 0.393
One solution was found :
x = 11/28 = 0.393