If 4g+ 5= 4/9, what is the value of 4g-2?
To find the value of 4g - 2, we first need to solve the equation 4g + 5 = 4/9 for g.
Let's start by isolating the variable g. We can do this by subtracting 5 from both sides of the equation:
4g + 5 - 5 = 4/9 - 5
4g = 4/9 - 45/9
Next, we need to find a common denominator for the fractions on the right side. The least common denominator (LCD) of 9 and 45 is 45. So, we rewrite both fractions with a denominator of 45:
4g = (4 * 5)/(9 * 5) - 45/9
4g = 20/45 - 45/9
Now, we need to find the least common multiple (LCM) of the denominators 45 and 9, which is 45. We can rewrite the fractions again with a denominator of 45:
4g = (20 - (5 * 45))/45
4g = (20 - 225)/45
Continuing to simplify, we have:
4g = (-205)/45
Finally, we can solve for g by dividing both sides of the equation by 4:
4g/4 = (-205)/45 / 4
g = (-205/45) * (1/4)
Multiplying the fractions:
g = (-205 * 1) / (45 * 4)
g = -205/180
g = -41/36
Now, we have found the value of g. To find the value of 4g - 2, we substitute g = -41/36 into the expression:
4g - 2 = 4 * (-41/36) - 2
4g - 2 = -164/36 - 2
Combining the terms:
4g - 2 = (-164 - 72)/36
4g - 2 = -236/36
Simplifying the fraction:
4g - 2 = (-59/9)
Therefore, the value of 4g - 2 is -59/9.