Grandma is removing weeds from her garden. She estimates that there are 250 weeds in the garden at the moment, and she can remove weeds at a rate of 5 per minute. At this rate, how many minutes will it take her to only have 30 weeds remaining in the garden?(3 points)
Equation:
Solution:
Meaning of the solution in words:
Let x be the number of minutes it takes Grandma to remove 30 weeds from the garden.
We know that she can remove weeds at a rate of 5 per minute.
So in x minutes, Grandma can remove 5x weeds from the garden.
Therefore, the equation can be written as 250 - 5x = 30.
Simplifying the equation, we get 220 - 5x = 0.
Moving the terms around, we get 5x = 220.
Dividing both sides by 5, we get x = 44.
Therefore, it will take Grandma 44 minutes to remove 30 weeds from the garden.
The Celsius to Fahrenheit formula: F=9/5C+32
Solve this formula for C. Check all answers that are true.
(4 points)
Responses
First step is to multiply by 9 on each side.
First step is to add 32 to both sides.
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5
Solution: 5/9F - 32 = C
To solve this equation for C, you would have to distribute at some point.
The correct steps to solve the formula F = 9/5C + 32 for C are as follows:
1. Subtract 32 from both sides: F - 32 = 9/5C
2. To isolate C, multiply both sides by 5/9 (or divide by 9/5): (F - 32) * (5/9) = C
So, the correct solution is C = (F - 32) * (5/9).
Checking all answers:
1. First step is to multiply by 9 on each side. - Not true, the first step is to subtract 32 from both sides.
2. First step is to add 32 to both sides. - Not true, the first step is to subtract 32 from both sides.
3. The next step from F - 32 = 9/5 C, could be to multiply both sides by 5. - Not true, the next step is to multiply both sides by 5/9.
4. The next step from F - 32 = 9/5 C, could be to divide both sides by 5. - True, this is the correct step.
The correct solution is C = (F - 32) * (5/9).
The Celsius to Fahrenheit formula: F=9/5C+32
Solve this formula for C. Check all answers that are true.
(4 points)
Responses
1 First step is to multiply by 9 on each side.
2 First step is to add 32 to both sides.
3 The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
4 The next step from F - 32 = 9/5 C, could be to divide both sides by 5
5 Solution: 5/9F - 32 = C
6 To solve this equation for C, you would have to distribute at some point.
To solve the Celsius to Fahrenheit formula F = (9/5)C + 32 for C, we need to perform the following steps:
1. First step is to subtract 32 from both sides: F - 32 = (9/5)C
2. The next step is to multiply both sides by 5/9 (or divide by 9/5): (F - 32) * (5/9) = C
So, the correct solution is C = (F - 32) * (5/9).
Now, let's check which statements are true:
1. First step is to multiply by 9 on each side. - False, the first step is to subtract 32 from both sides, not multiply by 9.
2. First step is to add 32 to both sides. - False, the first step is to subtract 32 from both sides, not add 32.
3. The next step from F - 32 = (9/5)C, could be to multiply both sides by 5. - False, the next step is to multiply both sides by 5/9, not 5.
4. The next step from F - 32 = (9/5)C, could be to divide both sides by 5. - False, the next step is to multiply both sides by 5/9, not divide by 5.
5. Solution: (5/9)F - 32 = C - True, this is the correct solution for C.
6. To solve this equation for C, you would have to distribute at some point. - False, there is no need to distribute in this equation.
Therefore, only Statement 5 is true: Solution: (5/9)F - 32 = C.
Izzie is trying to solve this inequality: 3(t+1)−4t≥−5
After she solves it, she shows it to you and asks you if she did it correctly.
This is the work she completed:
Step 1: 3t+3−4t≥−5
Step 2: −t+3≥−5
Step 3: −t≥−2
Step 4: t≤2
Izzie's work is partially correct, but she made a mistake in Step 3. Let's go through the steps again:
Step 1: Distribute 3 to both terms inside the parentheses:
3t + 3 - 4t ≥ -5
Step 2: Combine like terms:
-t + 3 ≥ -5
Step 3: Subtract 3 from both sides:
-t ≥ -5 - 3
-t ≥ -8
At this point, we need to remember that when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign needs to be flipped. Since we are dividing both sides by -1 (or multiplying by -1), the inequality sign will change direction.
Step 4: Multiply both sides by -1 (or divide by -1) and flip the inequality sign:
t ≤ 8
So the correct solution is t ≤ 8, not t ≤ 2.
Therefore, Izzie made a mistake in Step 4. The correct inequality is t ≤ 8.
5n−3<3(n+1)
To solve the inequality 5n - 3 < 3(n + 1), we will use the distributive property and then simplify the expression:
Step 1: Distribute 3 to both terms inside the parentheses:
5n - 3 < 3n + 3
Step 2: Combine like terms on both sides of the inequality:
5n - 3n < 3 + 3
Step 3: Simplify both sides of the equation:
2n < 6
Step 4: Divide both sides by 2 (the coefficient of n) to isolate n:
n < 6/2
Step 5: Simplify the right side of the equation:
n < 3
Therefore, the solution to the inequality is n < 3.
Solve the equation and inequality for x.
Part A: Solve the equation for x showing all steps for credit: ax−5=18
Part B: Solve the inequality for x showing all steps for credit: ax−5>18
Part C: State the difference between an equation and an inequality regarding solving steps and solution