Answer:
1/2(2x-6)= -6
Step-by-step explanation:
Multiply the two sides by the equation 2
2x-6=12
move the constant to the right hand side change sign
2x = -12 + 6
calculate the sum
2x= -6
Divide the 2 sides by 2
x= -3
Explanation:
It helps to understand the process of multiplying the binomials. Consider the simple case ...
(x +a)(x +b)
The product is ...
(x +a)(x +b) = x² +(a+b)x + ab
If the <em>constant</em> term (ab) is <em>negative</em>, the signs of (a) and (b) are <em>different</em>.
If the constant term (ab) is <em>positive</em>, the signs of (a) and (b) will both match the sign of the coefficient of the linear term (a+b).
___
Of course, the sum (a+b) will have the sign of the (a) or (b) value with the largest magnitude, so when the signs of (a) and (b) are different, the factor with the largest magnitude will have the sign of (a+b), the x-coefficient.
<u>Example</u>:
x² -x -6
-6 tells you the factors will have different signs. -x tells you the one with the largest magnitude will be negative.
-6 = -6×1 = -3×2 = ... (other factor pairs have a negative factor with a smaller magnitude)
The sums of these factor pairs are -5 and -1. We want the factor pair that has a sum of -1, the coefficient of x in the trinomial.
x² -x -6 = (x -3)(x +2)
Let k be a constant of proportionality. We can use the given information to write two equations:
24 = k/5 and 12 = k/10.
Solving for k gives k = 120 in both cases.
Let R be the unknown resistance when the current is 15 amperes:
15 = 120/R.
R = 120/15
R = 8 ohms.
Answer:
see explanation
Step-by-step explanation:
(1)
given
4x² = 81 ( divide both sides by 4 )
x² = 
( take the square root of both sides )
x = ± 
= ± 
---------------------------------------------------------------------
(2)
subtract 7 from both sides
(4x - 3)² = 32 ( take the square root of both sides )
4x - 3 = ± 
= ± 4
Add 3 to both sides
4x = 3 ± 4 ( divide both sides by 4 )
x = 
±
