AThe product of a number and 4 is the sum of the number and 4. Find the number. X = b. Write an algebraic expression for the following phrase. Use x to represent the unknown number. 6 less than two times a number.
The Correct Answer and Explanation is:
a. The product of a number and 4 is the sum of the number and 4. Find the number.
Let the unknown number be x.
We are told:
The product of a number and 4
= The sum of the number and 4
This translates to the equation: 4x=x+44x = x + 44x=x+4
Now solve the equation:
Step 1: Subtract x from both sides: 4x−x=x+4−x4x – x = x + 4 – x4x−x=x+4−x 3x=43x = 43x=4
Step 2: Divide both sides by 3: x=43x = \frac{4}{3}x=34
✅ Answer for part a: x=43\boxed{x = \frac{4}{3}}x=34
b. Write an algebraic expression for the following phrase:
“6 less than two times a number”
Let the unknown number be x.
“Two times a number” means:
2x2x2x
“6 less than” means subtract 6 from that quantity (important: “less than” reverses the order of subtraction)
So, the expression becomes: 2x−62x – 62x−6
✅ Answer for part b: 2x−6\boxed{2x – 6}2x−6
📘 300-Word Style Explanation:
In algebra, we often translate word problems into equations or expressions using variables. A variable, like x, stands for an unknown value that we are trying to find or represent.
Part a:
The statement says “the product of a number and 4”, which means we multiply the number by 4, or 4x. It also says this product is equal to the sum of the number and 4, or x + 4. We then write this relationship as an equation: 4x=x+44x = x + 44x=x+4
To solve, we use inverse operations. Subtract x from both sides to isolate like terms: 4x−x=3x=44x – x = 3x = 44x−x=3x=4
Then divide both sides by 3: x=43x = \frac{4}{3}x=34
Part b:
The phrase “6 less than two times a number” requires careful interpretation. Two times a number is written as 2x. The phrase “6 less than” means subtract 6 from the previous amount. So, the expression becomes: 2x−62x – 62x−6
In both parts, understanding the language used is key to writing correct mathematical models. Phrases like “less than”, “more than”, “product of”, and “sum of” each have specific meanings that help guide the setup of the expression or equation.
