Here is the next problem: Four less than twice a number equal to ten. What is the number
The Correct Answer and Explanation is:
Correct Answer:
The number is 7.
Explanation
To solve the equation “Four less than twice a number equals ten,” we begin by translating the words into a mathematical equation.
Let us represent the unknown number as x.
- “Twice a number” means 2 × x or 2x.
- “Four less than twice a number” means we subtract 4 from 2x, which gives 2x − 4.
- This expression is said to “equal ten,” which we write as an equation: 2x − 4 = 10
Now, we will solve this equation step-by-step.
Step 1: Add 4 to both sides of the equation
We want to isolate the term with the variable x, so we remove the −4 from the left side.
2x − 4 + 4 = 10 + 4
2x = 14
Step 2: Divide both sides by 2
Now, we divide both sides of the equation by 2 to solve for x.
2x ÷ 2 = 14 ÷ 2
x = 7
So, the number is 7.
Verification:
Let’s double-check our answer by substituting x = 7 back into the original word statement.
- Twice the number: 2 × 7 = 14
- Four less than 14: 14 − 4 = 10
This matches the original condition in the problem: “Four less than twice a number equals ten.”
This problem is an example of how algebra allows us to represent and solve real-world problems using variables and equations. The key steps involve correctly translating the words into math and solving the resulting equation by performing inverse operations, such as adding or dividing, to isolate the variable. This process builds a foundation for solving more complex algebraic equations later on.
