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
1. Start by distributing the 5 to the terms inside the parentheses:
5 * x + 5 * 3 - 7(x + 4) = 38
Simplify:
5x + 15 - 7(x + 4) = 38
2. Distribute the -7 to the terms inside the parentheses:
5x + 15 - 7x - 7 * 4 = 38
Simplify:
5x + 15 - 7x - 28 = 38
3. Combine like terms on the left side of the equation:
5x - 7x + 15 - 28 = 38
Simplify:
-2x - 13 = 38
4. Move the constant term to the right side of the equation by adding 13 to both sides:
-2x = 38 + 13
Simplify:
-2x = 51
5. Divide both sides of the equation by -2 to solve for x:
x = 51 / -2
6. Further simplify the solution:
x = -25.5
7. Verify the solution by substituting x = -25.5 back into the original equation and check if both sides are equal:
5(-25.5 + 3) - 7(-25.5 + 4) = 38
Simplify:
5(-22.5) - 7(-21.5) = 38
Solve:
-112.5 + 150.5 = 38
Both sides are equal, verifying that x = -25.5 is the solution to the equation.
that is not correct
Apologies for the mistake. Here is the correct step-by-step solution:
1. Start by distributing the 5 and -7 to the terms inside the parentheses:
5x + 15 - 7x - 28 = 38
2. Combine like terms on the left side of the equation:
(5x - 7x) + (15 - 28) = 38
-2x - 13 = 38
3. Move the constant term to the right side of the equation by adding 13 to both sides:
-2x = 38 + 13
-2x = 51
4. Divide both sides of the equation by -2 to solve for x:
x = 51 / -2
5. Simplify the solution:
x = -25.5
6. Verify the solution by substituting x = -25.5 back into the original equation and checking if both sides are equal:
5(-25.5 + 3) - 7(-25.5 + 4) = 38
Simplify the equation:
5(-22.5) - 7(-21.5) = 38
-112.5 + 150.5 = 38
Both sides are equal, verifying that x = -25.5 is the solution to the equation.
it's in a fraction form
Apologies again for the mistakes. Here is the correct step-by-step solution with the fraction form:
1. Start by distributing the 5 and -7 to the terms inside the parentheses:
5x + 15 - 7x - 28 = 38
2. Combine like terms on the left side of the equation:
(5x - 7x) + (15 - 28) = 38
-2x - 13 = 38
3. Move the constant term to the right side of the equation by adding 13 to both sides:
-2x = 38 + 13
-2x = 51
4. Divide both sides of the equation by -2 to solve for x:
x = 51 / -2
5. Simplify the solution:
x = -51 / 2
6. Verify the solution by substituting x = -51 / 2 back into the original equation and checking if both sides are equal:
5(-51/2 + 3) - 7(-51/2 + 4) = 38
Simplify the equation:
5(-51/2 + 6/2) - 7(-51/2 + 8/2) = 38
(-255/2 + 30/2) - (-357/2 + 56/2) = 38
(-255 + 30) / 2 - (-357 + 56) / 2 = 38
(-225) / 2 - (-301) / 2 = 38
-225 / 2 + 301 / 2 = 38
[(301 - 225) / 2] = 38
76 / 2 = 38
38 = 38
Both sides are equal, verifying that x = -51 / 2 is the solution to the equation.
Create A real-life problem of 7x -9 = 54 and solve it
Real-life problem:
Suppose you are planning a trip and you want to calculate the number of miles you can travel per hour if you have a certain amount of time available.
You have a total of 54 miles to cover on your trip. However, you need to factor in a delay of 9 hours due to unexpected circumstances.
To find out how fast you need to travel, you can use the equation 7x - 9 = 54, where x represents the number of miles you can travel per hour.
Solution:
1. Start with the equation 7x - 9 = 54.
2. Add 9 to both sides of the equation to isolate 7x on one side:
7x - 9 + 9 = 54 + 9
7x = 63
3. Divide both sides of the equation by 7 to solve for x:
7x / 7 = 63 / 7
x = 9
So, to cover the total distance of 54 miles within the available time, you need to travel at a speed of 9 miles per hour.