the result of doubling a number added to half and decreased by 1result to 20. Find the number
2x + 0.5x - 1 = 20
2.5x = 21
x = 8.4
8.4
To find the number, let's break down the given information and set up an equation.
First, we'll assign a variable to represent the unknown number. Let's call it "x."
According to the information given, "the result of doubling a number" can be expressed as "2x."
Next, we have "added to half." This can be expressed as "+ (1/2)."
Lastly, we have "decreased by 1," which can be expressed as "- 1."
Putting all the information together, we get the equation:
2x + (1/2) - 1 = 20
Now, let's solve this equation step by step to find the value of x.
First, we simplify the left side of the equation:
2x + (1/2) - 1 = 20
2x - (1/2) = 20 + 1
Next, we combine like terms:
2x - (1/2) = 21
To get rid of the fraction, we can multiply every term by 2:
2 * (2x - (1/2)) = 2 * 21
4x - 1 = 42
Next, we isolate the variable by moving -1 to the other side of the equation:
4x - 1 + 1 = 42 + 1
4x = 43
Finally, we solve for x by dividing both sides of the equation by 4:
4x/4 = 43/4
x = 10.75
So, the value of the unknown number is 10.75.