Four times a number, minus 8, is equal to two times the number, plus 12.
Let's represent the unknown number as "x".
The given equation is:
4x - 8 = 2x + 12
To simplify the equation, let's subtract 2x from both sides:
4x - 2x - 8 = 2x - 2x + 12
This simplifies to:
2x - 8 = 12
Next, let's add 8 to both sides:
2x - 8 + 8 = 12 + 8
This simplifies to:
2x = 20
Finally, let's divide both sides by 2 to solve for x:
(2x)/2 = 20/2
This simplifies to:
x = 10
Therefore, the unknown number is 10.
Let's solve the equation step by step:
Step 1: Let's assume the number is represented by the variable x.
Step 2: "Four times a number" can be written as 4x.
Step 3: "Minus 8" can be written as -8.
Step 4: "Two times the number" can be written as 2x.
Step 5: "Plus 12" can be written as +12.
Putting it all together, we have the equation:
4x - 8 = 2x + 12
Now, let's solve the equation:
Step 6: Subtract 2x from both sides to eliminate the 2x term:
4x - 2x - 8 = 2x - 2x + 12
Simplifying, we get:
2x - 8 = 12
Step 7: Add 8 to both sides:
2x - 8 + 8 = 12 + 8
Simplifying, we get:
2x = 20
Step 8: Divide both sides by 2 to solve for x:
(2x) / 2 = 20 / 2
Simplifying, we get:
x = 10
Therefore, the number is 10.
To solve this equation, let's start by defining the variable. Let's say the number is represented by "x".
The problem states that "four times a number, minus 8, is equal to two times the number, plus 12". This can be expressed as the equation:
4x - 8 = 2x + 12.
Now, let's isolate the variable "x" on one side of the equation. To do this, we want to get rid of the constant terms (numbers without variables) on both sides of the equation.
First, let's move the term with 2x to the left side of the equation by subtracting 2x from both sides:
4x - 2x - 8 = 2x - 2x + 12.
Simplifying this, we get:
2x - 8 = 12.
Next, let's isolate the term with 2x. To do this, we want to get rid of the constant term (-8) on the left side of the equation. We can do this by adding 8 to both sides:
2x - 8 + 8 = 12 + 8.
Simplifying this, we get:
2x = 20.
Finally, we can solve for "x" by dividing both sides of the equation by 2:
2x/2 = 20/2.
Simplifying this, we get:
x = 10.
So, the solution to the equation is x = 10.