Question

reasoning write and solve an equation to find the number.

two is subtracted from a number, and then the difference is divided by 3. the result is 30.

(2 - n) \div 3 = 30; -88
(n - 2) \div 3 = 30; 92
n - \frac{2}{3} = 30; 30.66
(n - 2) \div 3 = 30; 12

question 2
use properties of equality to solve the equation and check your solution.

\frac{22 - w}{3} = -7

w =

question 3
solve the equation. check your solution.

f + (-3) = -9

f =

Explanation:

🆕 New Concept Discovered: Translating Word Problems into Equations
Turning written clues into mathematical operations

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Step 1: Translate the word problem into an equation

Let the unknown number be represented by the variable \( n \).

• "Two is subtracted from a number" means we start with the number and subtract two:

$$ (n - 2) $$

• "and then the difference is divided by 3" means we take that entire result and divide it by 3:

$$ (n - 2) \div 3 $$

• "The result is 30" means this expression is equal to 30:

$$ (n - 2) \div 3 = 30 $$

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Step 2: Solve the equation for \( n \)

To find the value of \( n \), we undo the operations step-by-step:

1. Multiply both sides by 3 to undo the division:

$$ n - 2 = 30 \times 3 $$

$$ n - 2 = 92 $$

(Wait, let's calculate carefully: \( 30 \times 3 = 90 \))

$$ n - 2 = 90 $$

1. Add 2 to both sides to isolate \( n \):

$$ n = 90 + 2 $$

$$ n = 92 $$

Comparing this to the given options:

• \( (2 - n) \div 3 = 30;\ -88 \)
• \( (n - 2) \div 3 = 30;\ 92 \)
• \( n - \frac{2}{3} = 30;\ 30.66 \)
• \( (n - 2) \div 3 = 30;\ 12 \)

The correct option is the second one: \( (n - 2) \div 3 = 30;\ 92 \).

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Step 3: Solve Question 2

We are given the equation:

$$ \frac{22 - w}{3} = -7 $$

1. Multiply both sides by 3 to eliminate the fraction:

$$ 22 - w = -7 \times 3 $$

$$ 22 - w = -21 $$

1. Subtract 22 from both sides:

$$ -w = -21 - 22 $$

$$ -w = -43 $$

1. Multiply both sides by \(-1\):

$$ w = 43 $$

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Step 4: Solve Question 3

We are given the equation:

$$ f + (-3) = -9 $$

1. Simplify the addition of a negative number:

$$ f - 3 = -9 $$

1. Add 3 to both sides to isolate \( f \):

$$ f = -9 + 3 $$

$$ f = -6 $$

Answer:

• Question 1: \( (n - 2) \div 3 = 30;\ 92 \) (Second option)
• Question 2: \( w = 43 \)
• Question 3: \( f = -6 \)