4 times the sum of a number and-5 equals 24 what is the number
The correct answer and explanation is:
Correct Answer: 11
Explanation:
The problem states:
“Four times the sum of a number and negative five equals twenty-four.”
Let us define the unknown number as x. The phrase “the sum of a number and -5” translates to the expression (x + (−5)) or simply (x − 5).
The phrase “four times the sum” means we must multiply the expression (x − 5) by 4.
So the equation becomes:
4(x − 5) = 24
Now solve this equation step-by-step:
- Distribute the 4 to both terms inside the parentheses: 4 × x = 4x
4 × (−5) = −20 So,
4x − 20 = 24 - Add 20 to both sides of the equation to move the constant to the right-hand side: 4x − 20 + 20 = 24 + 20
4x = 44 - Divide both sides by 4 to isolate x: 4x ÷ 4 = 44 ÷ 4
x = 11
So the number is 11.
To check the solution:
Take the number 11.
Add −5 to it: 11 − 5 = 6
Multiply the result by 4: 6 × 4 = 24
The original condition is satisfied, so the answer is correct.
This type of equation represents a one-step algebraic equation involving distributive property and inverse operations. It is a basic skill in algebra to isolate variables and reverse operations using addition, subtraction, multiplication, and division. These techniques help solve for unknowns and are useful in both academic mathematics and practical problem solving in real life, such as budgeting, measuring, or adjusting quantities. Understanding how to build and solve such equations develops logical reasoning and confidence in handling more complex problems in algebra.