If 7 more than twice a number is 4 less than three times the same number, what is the number?
The correct answer and explanation is:
To solve the problem, we need to set up an equation based on the given conditions. The statement says:
“7 more than twice a number is 4 less than three times the same number.”
Let the unknown number be represented by the variable x.
- Twice a number is written as 2x.
- 7 more than twice a number is therefore 2x + 7.
- Three times the same number is written as 3x.
- 4 less than three times the number is written as 3x – 4.
The problem tells us that 7 more than twice a number equals 4 less than three times the same number. So, we can set up the equation: 2x+7=3x−42x + 7 = 3x – 4
Step-by-step solution:
Step 1: Isolate the variable (x) on one side of the equation.
To do this, subtract 2x from both sides of the equation to move all terms involving x to one side: 7=x−47 = x – 4
Step 2: Solve for x.
Next, add 4 to both sides to move the constant term to the other side: 7+4=x7 + 4 = x x=11x = 11
Final answer:
The number is 11.
Explanation:
We started by translating the verbal expression into a mathematical equation. Then, we solved for x by isolating it on one side of the equation. This method allows us to find the number that satisfies the given relationship between twice the number, three times the number, and the constants involved.