write the following as an equation. then solve.
twice the sum of a number and 9 is equal to three times the difference of the number and 9. find the number
Let's call the number "x".
The equation can be written as:
2(x + 9) = 3(x - 9)
Now let's solve for x:
2x + 18 = 3x - 27
Subtract 2x from both sides:
18 = x - 27
Add 27 to both sides:
45 = x
Therefore, the number is 45.
Step 1: Let's assume the number is represented by the variable x.
Step 2: "Twice the sum of a number and 9" can be written as 2(x + 9).
Step 3: "Three times the difference of the number and 9" is represented as 3(x - 9).
Step 4: Setting up the equation:
2(x + 9) = 3(x - 9)
Step 5: Solving the equation:
2x + 18 = 3x - 27
Subtracting 2x from both sides:
18 = x - 27
Adding 27 to both sides:
45 = x
Step 6: Therefore, the number is 45.
To write and solve the equation, let's start by defining the unknown number as "x."
The first part of the sentence states, "twice the sum of a number and 9." So, we can express this as:
2(x + 9)
The second part of the sentence says, "is equal to three times the difference of the number and 9." This can be written as:
3(x - 9)
Combining both parts, we have the equation:
2(x + 9) = 3(x - 9)
Now, let's solve the equation to find the value of "x."
Expanding the equation:
2x + 18 = 3x - 27
Rearranging the equation by moving all terms containing "x" to one side:
2x - 3x = -27 - 18
Simplifying:
-x = -45
Multiplying both sides by -1 to isolate "x":
x = 45
Therefore, the value of the number is 45.