Question

building & solving equations practice

1. elijah’s problem:

\i think of a number.
then i add 2.
then i multiply it by 3.
then i subtract 3.
then i divide the answer by 6.
my final answer is equal to the number i thought of at the beginning.\
a. write down an algebraic equation that represents this problem.
b. solve your equation to find the number elijah started with. show all of your work.

Explanation:

Part (a)

Step1: Define the variable

Let the number Elijah thought of be \( x \).

Step2: Translate each operation into algebra

• Add 2: \( x + 2 \)
• Multiply by 3: \( 3(x + 2) \)
• Subtract 3: \( 3(x + 2)-3 \)
• Divide by 6: \( \frac{3(x + 2)-3}{6} \)
• This equals the original number \( x \), so the equation is \( \frac{3(x + 2)-3}{6}=x \)

Step1: Simplify the left - hand side

First, expand the numerator: \( 3(x + 2)-3=3x+6 - 3=3x + 3 \)
So the equation becomes \( \frac{3x + 3}{6}=x \)

Step2: Eliminate the denominator

Multiply both sides of the equation by 6: \( 3x+3 = 6x \)

Step3: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 3=6x - 3x \)
Simplify the right - hand side: \( 3x=3 \)
Divide both sides by 3: \( x = 1 \)

Answer:

\( \boldsymbol{\frac{3(x + 2)-3}{6}=x} \)

Part (b)