Question

Four times a number increased by five is the same as triple the difference of a number and two. What is the number?

A.x=-11
B.x=-7
C.x=2
D.x=-1

Answer 1

To solve the equation, "Four times a number increased by five is the same as triple the difference of a number and two," we can follow these steps:

1. Assign a variable to represent the unknown number. Let's use x as the variable.

2. Translate the given information into an equation. "Four times a number increased by five" can be written as 4x + 5. "Triple the difference of a number and two" can be written as 3(x - 2).

3. Set up the equation by equating the two expressions: 4x + 5 = 3(x - 2).

4. Simplify the equation by distributing the 3 to both terms inside the parentheses: 4x + 5 = 3x - 6.

5. Combine like terms by subtracting 3x from both sides: x + 5 = -6.

6. Solve for x by subtracting 5 from both sides: x = -11.

Based on these steps, the value of x that satisfies the equation is x = -11. Therefore, the correct answer is A. x = -11.

Explanation:

Answer 2

To solve the equation, "Four times a number increased by five is the same as triple the difference of a number and two," we can follow these steps:

1. Assign a variable to represent the unknown number. Let's use x as the variable.

2. Translate the given information into an equation. "Four times a number increased by five" can be written as 4x + 5. "Triple the difference of a number and two" can be written as 3(x - 2).

3. Set up the equation by equating the two expressions: 4x + 5 = 3(x - 2).

4. Simplify the equation by distributing the 3 to both terms inside the parentheses: 4x + 5 = 3x - 6.

5. Combine like terms by subtracting 3x from both sides: x + 5 = -6.

6. Solve for x by subtracting 5 from both sides: x = -11.

Based on these steps, the value of x that satisfies the equation is x = -11. Therefore, the correct answer is A. x = -11.