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
To solve the equation 5(x+3) - 7(x-4) = 38, the following steps can be followed:
1. Distribute the coefficients to the terms inside the parentheses:
5x + 15 - 7x + 28 = 38
2. Combine like terms on both sides of the equation:
(5x - 7x) + (15 + 28) = 38
-2x + 43 = 38
3. Simplify the equation by subtracting 43 from both sides:
-2x = 38 - 43
-2x = -5
4. Divide both sides of the equation by -2 to isolate the variable, x:
x = -5 / -2
x = 2.5
To create a real-life situation for the equation 8(x+9) = 144, let's consider the scenario where a store is offering a discount. The original price of an item is multiplied by 8 and then increased by $9 to be equal to $144, which is the discounted price. We are required to find the original price.
To solve the equation, we can use two different methods:
Method 1: Distributive Property and Simplification
1. Distribute the coefficient 8 to the term inside the parentheses:
8x + 72 = 144
2. Subtract 72 from both sides of the equation:
8x = 144 - 72
8x = 72
3. Divide both sides of the equation by 8 to isolate the variable, x:
x = 72 / 8
x = 9
Method 2: Division
1. Divide both sides of the equation by 8 to isolate the term inside the parentheses:
x + 9 = 144 / 8
x + 9 = 18
2. Subtract 9 from both sides of the equation:
x = 18 - 9
x = 9
Both methods yield the same solution, x = 9.
Personally, I prefer Method 2: Division, because it simplifies the equation directly by dividing both sides, making it less likely to make errors or encounter intermediate steps that may introduce mistakes. Additionally, it requires fewer steps, which can lead to a quicker solution.
can you make this sound like a 7th grader
Sure! Here are the steps to solve the equation 5(x+3) - 7(x-4) = 38 in a more casual and simplified way:
1. Do the stuff inside the parentheses first, so we have 5 times (x + 3) and 7 times (x - 4).
2. Multiply the numbers outside of the parentheses by the numbers inside. So it's like 5 times x plus 5 times 3, and 7 times x minus 7 times 4.
3. Combine the numbers together. So it's like 5 times x plus 15, and 7 times x minus 28.
4. Now we can do the subtraction. So it's like 5x plus 15 minus 7x plus 28, and that should equal 38.
5. Add or subtract all the similar terms together. So it's like 5x minus 7x plus 15 plus 28 equals 38.
6. Combine the numbers and solve for x. So it's like -2x plus 43 equals 38.
7. We need to get x by itself, so minus 43 from both sides. So it's like -2x equals 38 minus 43.
8. Simplify and solve for x. So it's like -2x equals -5.
9. Finally, divide both sides by -2 to find x. So it's like x equals -5 divided by -2.
For the equation 8(x+9) = 144, let's imagine that there's a store giving a discount on an item. The original price, represented by x, is multiplied by 8, and then $9 is added to the result, equaling $144, which is the discounted price. We need to find the original price.
To solve this, there are two ways we can do it:
Method 1: Using the Distributive Property and Simplification
1. First, take the number outside of the parentheses, which is 8, and multiply it by each number inside. So it's like 8 times (x + 9).
2. Multiply the numbers and simplify, which gives us 8x + 72.
3. Now, we can write the equation as 8x + 72 = 144.
4. To find x, we need to get rid of the 72. So we subtract 72 from both sides to make it 8x = 144 - 72.
5. Simplify and solve for x, which gives us 8x = 72.
6. Since we want x alone on one side, divide both sides by 8. So it's like x = 72 divided by 8.
7. Finally, simplify and find x. So it's like x = 9.
Method 2: Using Division
1. We can divide the whole equation by 8 to make it easier. So it's like 8(x + 9) divided by 8 equals 144 divided by 8.
2. That simplifies to x + 9 equals 18.
3. To find x, subtract 9 from both sides of the equation. So it's like x equals 18 minus 9.
4. Simplify and find x, which gives us x = 9.
In both methods, we find that x equals 9.
I personally like Method 2: Using Division more because it's a quicker way to find the solution. It also simplifies the equation more directly, which reduces the chances of making mistakes along the way.
can you make it shorter
Sure! Here are the steps to solve the equation 5(x+3) - 7(x-4) = 38 in a shorter and simpler way:
1. Distribute the coefficients to the terms inside the parentheses.
2. Combine like terms on both sides of the equation.
3. Simplify the equation by subtracting or adding numbers to both sides.
4. Isolate the variable, x, by dividing or subtracting numbers as necessary.
5. Solve for x.
For the equation 8(x+9) = 144:
1. Distribute the coefficient to the term inside the parentheses.
2. Simplify the equation by combining like terms.
3. Isolate the variable, x, by subtracting or dividing numbers.
4. Solve for x.
Both methods should yield the same solution.
I personally prefer using shorter and simpler steps because they are easier to follow and understand. They also reduce the chances of making mistakes during the solving process.