Answer :
To determine which step is not algebraically correct when solving for [tex]\( t \)[/tex], let's analyze each step carefully.
### Step 1:
[tex]\[ w \cdot r_1 \cdot t = r_2 \cdot t \][/tex]
To isolate [tex]\( t \)[/tex], we can divide both sides of the equation by [tex]\( t \)[/tex], assuming [tex]\( t \neq 0 \)[/tex]:
[tex]\[ w \cdot r_1 = r_2 \][/tex]
This is algebraically correct.
### Step 2:
[tex]\[ w = t \cdot (r_1 + r_2) \][/tex]
To solve for [tex]\( t \)[/tex], we divide both sides by [tex]\( (r_1 + r_2) \)[/tex], assuming [tex]\( r_1 + r_2 \neq 0 \)[/tex]:
[tex]\[ t = \frac{w}{r_1 + r_2} \][/tex]
This is also algebraically correct.
### Step 3:
[tex]\[ w = r_1 \cdot r_2 \cdot t \][/tex]
To solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{w}{r_1 \cdot r_2} \][/tex]
However, this step is not correct given the original equation. The relationship described by [tex]\( w = r_1 \cdot r_2 \cdot t \)[/tex] doesn't match the structure of the original equation [tex]\( w \cdot r_1 \cdot t = r_2 \cdot t \)[/tex], and therefore the manipulation of the variables leads to an incorrect representation.
### Conclusion:
The third step:
[tex]\[ w = r_1 \cdot r_2 \cdot t \][/tex]
is not algebraically correct when solving for [tex]\( t \)[/tex].
So, the incorrect step is:
[tex]\[ \boxed{3} \][/tex]
### Step 1:
[tex]\[ w \cdot r_1 \cdot t = r_2 \cdot t \][/tex]
To isolate [tex]\( t \)[/tex], we can divide both sides of the equation by [tex]\( t \)[/tex], assuming [tex]\( t \neq 0 \)[/tex]:
[tex]\[ w \cdot r_1 = r_2 \][/tex]
This is algebraically correct.
### Step 2:
[tex]\[ w = t \cdot (r_1 + r_2) \][/tex]
To solve for [tex]\( t \)[/tex], we divide both sides by [tex]\( (r_1 + r_2) \)[/tex], assuming [tex]\( r_1 + r_2 \neq 0 \)[/tex]:
[tex]\[ t = \frac{w}{r_1 + r_2} \][/tex]
This is also algebraically correct.
### Step 3:
[tex]\[ w = r_1 \cdot r_2 \cdot t \][/tex]
To solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{w}{r_1 \cdot r_2} \][/tex]
However, this step is not correct given the original equation. The relationship described by [tex]\( w = r_1 \cdot r_2 \cdot t \)[/tex] doesn't match the structure of the original equation [tex]\( w \cdot r_1 \cdot t = r_2 \cdot t \)[/tex], and therefore the manipulation of the variables leads to an incorrect representation.
### Conclusion:
The third step:
[tex]\[ w = r_1 \cdot r_2 \cdot t \][/tex]
is not algebraically correct when solving for [tex]\( t \)[/tex].
So, the incorrect step is:
[tex]\[ \boxed{3} \][/tex]
