Answer:
1. A) Swap sides 4= -2/3x-4 to -2/3x-4=4
B) Group all constants on the right side of the equation
-2/3 times x=4+4
c) Add 4 to both sides:
-2/3x--4+4=4+4
D) Simplify the arithmetic:
-2/3 times x = 4+4
E ) Simplify the arithmetic:
-2/3 timws x =8
F) Isolate the x: -2/3 times x =8
G) Multiply both sides by inverse fraction 3/-2
-2/3x times 3/-2=8 times 3/-2
H) Simplify the signs:
-2/3 times x times -3/2=8 times 3/-2
I) Group like terms:
-2/3 times -3/2 x=8 times 3/-2
J) Simplify the arithmetic:
1x=8 times 3/-2
K) Simplify the left side:
x=8 times -3/2
L) simplify the signs
x=8 times 3/-2
N) Multiply the fractions:
x= 8(-3)/2
Answer to number one is X=-12
Number 2:
1) Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-6/7*x-(-4)-(-2)=0
2)
Simplify 6/7
3)
((0 - (6/7 • x)) - -4) - -2 = 0
4) Subtracting a whole from a fraction
Rewrite the whole as a fraction using 7 as the denominator :
-4= -4/1 = -4 times 7/ 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
5) 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:
-6x- (-4 times 7) / 7 = 28-6x/ 7
6) (28 -6x) / 7 - -2 =0
7) Subtracting a whole from a fraction
Rewrite the whole as a fraction using 7 as the denominator :
-2= -2/1= -2 times 7/ 7
8) Pull out like factors :
28 - 6x = -2 • (3x - 14)
9) Adding up the two equivalent fractions
-2 times ( 3x-14) - (-2 times 7) / 7 = 42-6x /7
10)
Pull out like factors :
42 - 6x = -6 • (x - 7)
11) -6 times ( x-7) / 7 =0
12) 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 multiplys both sides of the equation by the denominator.
Here's how:
-6•(x-7)/7 • 7 = 0 • 7
Now, on the left hand side, the 7 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-6 • (x-7) = 0
13) Solve : -6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
14) Solve : x-7 = 0
Add 7 to both sides of the equation :
x = 7
