The equation 1/14 (196x+17-10)=______ (20x+12x) has no solution. The equation (4x+24/122)=_____ (x+16/122)
1/14 (196x+17-10)= (14/20)(20x+12x)
has no solution since
(14/20)(20x+12x) = 14x + 42/5
and
1/14 (196x+17-10) = 14x + 1/2
and
there is no value of x such that
14x+42/5 = 14x + 1/2
To solve the first equation, let's simplify the expression on the left side first. We have:
1/14 (196x+17-10) = 1/14 (196x+7)
Next, let's simplify the expression on the right side:
(20x+12x) = 32x
So now we have the equation:
1/14 (196x+7) = 32x
To solve this equation, we can multiply both sides of the equation by 14 to eliminate the fraction:
14 * (1/14 (196x+7)) = 14 * (32x)
This simplifies to:
196x + 7 = 448x
Now, let's move the variables to one side of the equation and the constant terms to the other side:
196x - 448x = -7
Simplifying further:
-252x = -7
To isolate x, we can divide both sides of the equation by -252:
-252x / -252 = -7 / -252
This gives us:
x = 7/252
Therefore, the solution for the first equation is x = 7/252.
Moving on to the second equation:
(4x+24)/122 = (x+16)/122
The denominator is the same for both sides, so we can simply equate the numerators:
4x + 24 = x + 16
Now, let's move the variables to one side and the constant terms to the other side:
4x - x = 16 - 24
This simplifies to:
3x = -8
To isolate x, we can divide both sides of the equation by 3:
3x / 3 = -8 / 3
This gives us:
x = -8/3
Therefore, the solution for the second equation is x = -8/3.