You have been given the following equation to solve as a challenge by your friend. Create a list of steps that you could follow to find the solution. Make sure to include all steps in the correct order.
5(x+3)−7(x−4)=38
Write a real-life situation to fit the following equation. Then, solve the equation in two different ways. Show all the steps. Finally, choose which solution method you liked best and explain your reason.
8(x+9)=144
Steps to solve the equation 5(x+3)−7(x−4)=38:
1. Distribute the 5 and the -7:
5x + 15 - 7x + 28 = 38
2. Combine like terms:
-2x + 43 = 38
3. Subtract 43 from both sides of the equation:
-2x = -5
4. Divide both sides by -2:
x = 5/2 or x = 2.5
Real-life situation: You have a coupon for a store that gives you a 20% discount on all purchases. You want to buy a shirt that costs $30. Write an equation for this situation and solve it using two different methods.
Equation:
The equation we can create is:
0.8 * x = 30
Method 1 - Multiplication:
1. Multiply both sides of the equation by 0.8:
0.8 * 0.8 * x = 0.8 * 30
2. Simplify and solve for x:
x = 24
Method 2 - Division:
1. Divide both sides of the equation by 0.8:
x = 30 / 0.8
2. Simplify and solve for x:
x = 37.5
Preferred Solution Method: I prefer Method 1 - Multiplication. This method allows me to isolate the variable (x) on one side of the equation and directly solve for it. It is a more straightforward approach and usually yields a more precise solution. In this case, it gave a whole number solution (24), which is more appropriate for a real-life situation like purchasing a shirt.