Final answer:
To solve the equation 2/5(x-1/2)=-2 3/4, we convert all numbers into improper fractions, perform the operation by multiplying both sides by the reciprocal of 2/5 and simplifying. The solution for 'x' is -6 3/8.
Step-by-step explanation:
To solve the equation 2/5(x-1/2)=-2 3/4, we need to perform several steps to isolate 'x'. First, let's convert all mixed numbers and fractions into improper fractions to make it easier to perform operations.
Firstly, the mixed number -2 3/4 can be converted into an improper fraction by multiplying the whole number by the denominator, adding the numerator, and writing the result over the original denominator:
Now substitute this into the original equation:
Multiply both sides of the equation by the reciprocal of 2/5, which is 5/2, to cancel it out on the left side:
- 5/2 * 2/5(x - 1/2) = 5/2 * -11/4
- (x - 1/2) = -55/8
Next, we need to get rid of the fraction on the left side by adding 1/2 to both sides:
- (x - 1/2) + 1/2 = -55/8 + 1/2
- x = -55/8 + 4/8
- x = -51/8
The solution to the equation is x = -51/8, which is an improper fraction. To write this as a mixed number in its simplest form, divide the numerator by the denominator:
- -51 ÷ 8 = -6 with a remainder of 3
- So, x = -6 3/8