Show that 2 10
—— = ——
4 - x 4 + x
Is equivalent to 12x = 32 for all values of x not equal to 4 or -4.
2/(4-x) = 10/ (4+x) ???? if x is 4 or - 4 blows up, zero denominator
so
40 - 10 x = 8 + 2 x
32 = 12 x
To show that the equation 2/(4 - x) = 10/(4 + x) is equivalent to 12x = 32 for all values of x not equal to 4 or -4, we need to cross-multiply and simplify the equation.
1. Start with the equation: 2/(4 - x) = 10/(4 + x)
2. Cross-multiply by multiplying the numerator on the left side with the denominator on the right side and vice versa.
(2) * (4 + x) = (10) * (4 - x)
Simplified: 8 + 2x = 40 - 10x
3. Combine like terms by moving all the terms involving x to one side of the equation.
2x + 10x = 40 - 8
Simplified: 12x = 32
Therefore, we have shown that the equation 2/(4 - x) = 10/(4 + x) is equivalent to 12x = 32 for all values of x not equal to 4 or -4.
To show that the equation (2 / (4 - x)) = (10 / (4 + x)) is equivalent to 12x = 32 for all values of x not equal to 4 or -4, we need to cross-multiply and simplify both sides.
First, cross-multiply the equation:
2 * (4 + x) = 10 * (4 - x)
Simplifying both sides:
8 + 2x = 40 - 10x
Now, let's isolate the variable x on one side of the equation:
2x + 10x = 40 - 8
Combining like terms:
12x = 32
Hence, we have shown that the equation (2 / (4 - x)) = (10 / (4 + x)) is equivalent to 12x = 32 for all values of x not equal to 4 or -4.