Writing and Solving Multi-Step Equations

We want to write an equation that represents the given situation. We will represent the unknown quantity with a variable. Here, the unknown quantity is the starting value of Emily's investment, which we will call v. We know that after the first week, the value of the investment fell by $25. This means that the value after the first week is v-25. Value After First Week: v-25 During the second week, the value of the investment doubled, so the value of the investment after the second week is 2(v-25). Value After First Week:& v-25 Value After Second Week:& 2(v-25) Finally, the value rose by $30 during the last week, meaning that the final value of the investment is 2(v-25)+30. Value After First Week:& v-25 Value After Second Week:& 2(v-25) Value After Third Week:& 2(v-25)+30 We know that the final value of the investment is $130. Let's use this information to write an equation. 2(v-25)+30=130 This equation can help us find the original value of the investment. Note that we can write different equations, but they will all be equivalent to the equation we wrote here. These equivalent equations can also be obtained by applying Properties of Equality to the above equation.

We want to write an equation that represents the given situation. We first represent the unknown quantity with a variable. Here, the unknown quantity is the distance that Ignacio ran on the first day, which we will call d. Total Distance After One Day:& d On the second day, Ignacio ran 4 miles. This means that the total distance after two days was d+4 miles. Total Distance After One Day:& d Total Distance After Two Days:& d+4 We know that Ignacio doubled the distance he ran on the two previous days on Day 3. The total distance after three days was 2(d+4) miles. Total Distance After One Day:& d Total Distance After Two Days:& d+4 Total Distance After Three Days:& 2(d+4) On the final day, Ignacio ran 3 miles. Total Distance After One Day:& d Total Distance After Two Days:& d+4 Total Distance After Three Days:& 2(d+4) Total Distance After Four Days:& 2(d+4) + 3 We also know that Ignacio ran 21 miles over the whole challenge, so let's set our expression equal to 21. 2(d+4)+3=21 Note that we can write different equations, but they will all be equivalent to the equation we wrote. These equivalent equations can also be found by applying the Properties of Equality to the one we found.

We want to write an equation that represents the given situation. We will represent the unknown quantity with a variable. Here, the unknown quantity is the starting value of each investment, which we will call v. Initial Value:& v Tearrik's investment fell in value by $20 in the first week, so its value was v-20 at that point. The value then tripled over the next week. The final value of Tearrik's investment is 3(v-20). Initial Value:& v Value of Tearrik's Investment:& 3(v-20) Ramsha's investment grew by a quarter during the first week, so the value of the investment was 54v. In the second week, the value grew by $10, so the final value is 54v+10. Initial Value:& v [0.5em] Value of Tearrik's Investment:& 3(v-20) [0.5em] Value of Ramsha's Investment:& 5/4v+10 We know that the final values of both investments were the same, so let's set these expressions equal to each other to write an equation. 3(v-20)=5/4v+10 Note that we can write different equations, but they will all be equivalent to the equation we wrote. These equivalent equations can also be obtained by applying the Properties of Equality to our equation.

We want to write an equation that represents the given situation. We first represent the unknown quantity with a variable. Here, the unknown quantity is the usual distance that Maya runs, which we will call d. Usual Distance:& d On Thursday, Maya wanted to run twice the distance she usually runs, or 2d miles. However, she ended up running 3 miles less than planned, so she ran 2d-3 miles. Usual Distance:& d Distance on Thursday:& 2d-3 On Saturday, Maya ran 3 miles more than she usually does. This means that she ran d+3 miles. Usual Distance:& d Distance on Thursday:& 2d-3 Distance on Saturday:& d+3 We know that the two distances are equal, so let's set them equal to each other to write an equation. 2d-3=d+3 Note that we can write different equations, but they will all be equivalent to the equation we wrote. These equivalent equations can also be written by applying the Properties of Equality to our equation here.