Answer:
(-2x ÷ 5) - (9/5 ÷ 5) = -2/5 * x - 9/25
Explanation:
To solve the expression (2x - 2 1/5 - -4) ÷ -5, we need to follow the order of operations, also known as PEMDAS.
1. First, simplify the expression inside the parentheses (-2 1/5 - -4).
To subtract a negative number, we can change it to addition. So, (-2 1/5 - -4) becomes (-2 1/5 + 4).
Next, let's convert the mixed number -2 1/5 to an improper fraction.
-2 1/5 = -11/5
Now we can add the fractions: -11/5 + 4.
To add these fractions, we need a common denominator. The least common denominator for 5 and 1 is 5.
-11/5 + 4/1 = -11/5 + 20/5 = 9/5
Therefore, (-2 1/5 - -4) simplifies to 9/5.
2. Now, let's substitute the simplified expression back into the original expression: (2x + 9/5).
3. Finally, divide the expression by -5: (2x + 9/5) ÷ -5.
To divide by a negative number, we can multiply the expression by -1 and then divide by 5.
(2x + 9/5) ÷ -5 = (-1)(2x + 9/5) ÷ 5
Applying the distributive property, we get:
(-1)(2x + 9/5) ÷ 5 = (-2x - 9/5) ÷ 5
To divide by 5, we can multiply each term by 1/5:
(-2x - 9/5) ÷ 5 = (-2x ÷ 5) - (9/5 ÷ 5)
Simplifying further:
-2x ÷ 5 = -2/5 * x
9/5 ÷ 5 = 9/25
Therefore, the final answer is:
(-2x ÷ 5) - (9/5 ÷ 5) = -2/5 * x - 9/25
Please note that this is the simplified form of the expression, assuming that no specific value for x is given.