1/4 x (7+3g)= - g/8
please help
To solve the equation 1/4 x (7+3g) = -g/8, we can follow these steps:
Step 1: Distribute the 1/4 to the terms inside the parentheses:
(1/4) x 7 + (1/4) x (3g) = -g/8
This simplifies to:
7/4 + (3/4)g = -g/8
Step 2: Common denominator
To manipulate the equation more easily, it is helpful to find the common denominator for the fractions involved. The least common denominator (LCD) in this case is 4 x 8 = 32. Multiply each term by the necessary factors to get the LCD:
(7/4) x 8 + (3/4)g x 8 = -(g/8) x 32
This simplifies to:
56/4 + 24g/4 = -4g
Step 3: Simplify the equation:
14 + 6g = -4g
Step 4: Combine like terms:
14 + 6g + 4g = 0
Step 5: Move all the terms with variables to one side of the equation:
6g + 4g + 4g = -14
Simplifying further:
14g = -14
Step 6: Solve for g:
Divide both sides by 14 to isolate g:
g = -14/14
Finally, simplify:
g = -1
The solution to the equation is g = -1.