Alright — let's do this. a) $2 \times \Delta + 13 = 37$ Step 1: Isolate the term with $\Delta$. $$2 \times \Delta = 37 - 13$$ $$2 \times \Delta = 24$$ Step 2: Solve for $\Delta$. $$\Delta = \frac{24}{2}$$ $$\Delta = 12$$ Using the train and improvement method: | problem solution ($\Delta$) | test | conclusion | |---|---|---| | $10$ | $2 \times 10 + 13 = 20 + 13 = 33$ | $33 < 37$, too low | | $15$ | $2 \times 15 + 13 = 30 + 13 = 43$ | $43 > 37$, too high | | $12$ | $2 \times 12 + 13 = 24 + 13 = 37$ | $37 = 37$, correct | The solution is $\boxed{\Delta = 12}$. b) $14 \times \Delta - 21 = 77$ Step 1: Isolate the term with $\Delta$. $$14 \times \Delta = 77 + 21$$ $$14 \times \Delta = 98$$ Step 2: Solve for $\Delta$. $$\Delta = \frac{98}{14}$$ $$\Delta = 7$$ Using the train and improvement method: | problem solution ($\Delta$) | test | conclusion | |---|---|---| | $5$ | $14 \times 5 - 21 = 70 - 21 = 49$ | $49 < 77$, too low | | $10$ | $14 \times 10 - 21 = 140 - 21 = 119$ | $119 > 77$, too high | | $7$ | $14 \times 7 - 21 = 98 - 21 = 77$ | $77 = 77$, correct | The solution is $\boxed{\Delta = 7}$. Send me the next one 📸