Use the given information to write an equation. let x represent the number described in the exercise. The difference between two-fifths of a number and 5 is seven-fifths of that number. write the equation and solve.
2/5 x - 5=7/5 x
multiplyihg both sides of the equation by 5
2x-25=7x
subtracting 2 x from each side
-25=5x
x=-5
To write the equation, let's break down the given information into mathematical expressions:
1) "Two-fifths of a number": This can be represented as (2/5)x.
2) "The difference between two-fifths of a number and 5": This can be represented as (2/5)x - 5.
3) "Seven-fifths of that number": This can be represented as (7/5)x.
Based on the given information, the equation can be written as:
(2/5)x - 5 = (7/5)x
To solve this equation, we can eliminate the fractions by multiplying every term by a common denominator, which in this case is 5:
5 * [(2/5)x - 5] = 5 * [(7/5)x]
Simplifying the equation, we get:
2x - 25 = 7x
To isolate the variable x, we can subtract 2x from both sides of the equation:
2x - 25 - 2x = 7x - 2x
-25 = 5x
Finally, we can solve for x by dividing both sides of the equation by 5:
-25/5 = 5x/5
-5 = x
Therefore, the solution is x = -5.
To write the equation, we will break down the information given:
1. Let x represent the number described.
2. Two-fifths of the number: (2/5)x
3. The difference between two-fifths of the number and 5: (2/5)x - 5
4. Seven-fifths of the number: (7/5)x
Putting it all together, the equation becomes:
(2/5)x - 5 = (7/5)x
To solve this equation for x, we will eliminate the fractions by multiplying every term by the least common denominator (LCD), which is 5 in this case:
5 * [(2/5)x - 5] = 5 * [(7/5)x]
This simplifies to:
2x - 25 = 7x
Next, we'll isolate x by moving the terms involving x to one side:
2x - 7x = 25
Simplifying further:
-5x = 25
To find the value of x, divide both sides of the equation by -5:
x = 25 / (-5)
Therefore, x = -5.
The solution to the equation is x = -5.