Math CentralQuandaries & Queries


Question from Monejah, a student:

I need help solving 8t-r=12t for t

Hi Monejah,

Solve it first with a specific value for $r,$ say $r = 7.$

Solve $8t - 7 = 12t$ for $t.$

You want to isolate $t$ on the left of the equality sign so you need to remove the term $12t$ from the right side. To do this add $-12t$ to both sides of the equation to get

\[8t - 7 - 12t = 12t - 12t\]

simplifying gives

\[-4t - 7 = 0\]

Now add 7 to each side to get

\[-4 t = 7\]

Finally multiply each side by $\large - \frac14$ to get

\[- \frac14 \times -4 t = - \frac14 \times 7\]


\[t = - \frac74\]

Now mimic these steps to solve $8t - r = 12t$ for $t.$


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