Below is the equation that represents the markers Janelle brought in for her math group.
x = the number of students in Janelle's math group.
3x + 5 = 23
Solve the equation to determine how many students are in Janelle's group?
Starting with the equation:
3x + 5 = 23
Subtracting 5 from both sides:
3x = 18
Dividing both sides by 3:
x = 6
Therefore, there are 6 students in Janelle's math group.
Consider this equation:
–2x – 4 + 5x = 8
Generate a plan to solve for the variable. Describe the steps that will be used.
To solve for the variable in the equation -2x - 4 + 5x = 8, we can use the following steps:
1. Combine like terms on the left side of the equation. In this case, we can combine the -2x and 5x terms:
-2x + 5x = 3x
2. Add 4 to both sides of the equation to isolate the variable:
-2x + 5x + 4 = 8 + 4
Simplifying:
3x + 4 = 12
3. Finally, isolate the variable by subtracting 4 from both sides of the equation:
3x + 4 - 4 = 12 - 4
Simplifying:
3x = 8
4. To find the value of the variable x, divide both sides of the equation by 3:
3x/3 = 8/3
Simplifying:
x = 8/3
Therefore, the solution to the equation -2x - 4 + 5x = 8 is x = 8/3.
1. Combine like terms on the left side of the equation. In this case, we can combine the -2x and 5x terms:
-2x + 5x = 3x
2. Add 4 to both sides of the equation to isolate the variable:
-2x + 5x + 4 = 8 + 4
Simplifying:
3x + 4 = 12
3. Finally, isolate the variable by subtracting 4 from both sides of the equation:
3x + 4 - 4 = 12 - 4
Simplifying:
3x = 8
4. To find the value of the variable x, divide both sides of the equation by 3:
3x/3 = 8/3
Simplifying:
x = 8/3
Therefore, the solution to the equation -2x - 4 + 5x = 8 is x = 8/3.
Yes, that's correct.
Julissa gave out an equal number of oranges to each of the 6 apartments on her floor. If she gave each apartment 5 oranges, how many oranges did Julissa give out in all?
StartFraction 5 Over 6 EndFraction
1 and one-fifth
11
Julissa gave out a total of:
5 oranges per apartment x 6 apartments = 30 oranges in all.
Therefore, Julissa gave out 30 oranges in all.
Oksana wrote the equation below on the whiteboard.
6 b + 6 = 48
What is the value of b?
4
7
8
9
To solve for b in the equation 6b + 6 = 48, we can use the following steps:
1. Subtract 6 from both sides of the equation:
6b + 6 - 6 = 48 - 6
Simplifying:
6b = 42
2. To find the value of b, divide both sides of the equation by 6:
6b/6 = 42/6
Simplifying:
b = 7
Therefore, the value of b in the equation 6b + 6 = 48 is b = 7.
So, the answer is 7.
Mrs. McAlister wrote the equation 10 t minus 4 t + 3 t = 8 on the board and asked students to write an equivalent equation. The table below shows the responses from four students.
Student Responses
Name
Equation
Michele
3 t = 8
Piotr
6 t = 8
Ronnie
Negative 1 t = 8
Tanisha
9 t = 8
Which student wrote an equation that is equivalent to Mrs. McAlister’s?
Michele
Piotr
Ronnie
Tanisha
To determine which student wrote an equation that is equivalent to Mrs. McAlister's equation 10t - 4t + 3t = 8, we need to simplify the left side and solve for t:
10t - 4t + 3t = 8
Simplifying:
9t = 8
To find the value of t, we divide both sides of the equation by 9:
t = 8/9
Therefore, the student who wrote an equivalent equation is Tanisha, with 9t = 8.
Shau-uen solved the equation 18.5 w + 6.5 w minus 2.8 w = 149.1. Her work is shown below.
Step 1 18.5 w + 6.5 w minus 2.8 w = 149.10
Step 2 25 w minus 2.8 w = 149.1
Step 3 Negative 2.8 w = 5.964
Step 4 w = negative 2.13
In which step did Shau-uen make her first error?
Step 1
Step 2
Step 3
Step 4
Shau-uen made her first error in Step 2.
In Step 1, she correctly added the terms 18.5w, 6.5w, and -2.8w. However, in Step 2, she incorrectly subtracted 2.8w from 25w.
The correct simplification in Step 2 would be:
18.5w + 6.5w - 2.8w = 149.1
(18.5w + 6.5w) - 2.8w = 149.1
25w - 2.8w = 149.1
Therefore, the error was made in Step 2.
Which expression is equivalent to 7 b + 4 b minus 1 b?
2b
4b
10b
12b
Combining like terms in the expression 7b + 4b - 1b, we get:
7b + 4b - 1b = (7b + 4b) - 1b = 11b - 1b = 10b
Therefore, the expression 7b + 4b - 1b is equivalent to 10b.
Melisande collected 14 bottles on Saturday and 9 bottles on Sunday for recycling. On Monday, she took all the bottles to the recycling center, where they paid her a certain amount, b, for each bottle. However, she had to pay the recycling center a one-time service fee of $0.25. If she left there with $3.20 for the bottles, what is the value of b?
$0.14
$0.15
$0.23
$0.69
The total number of bottles Melisande collected is:
14 bottles + 9 bottles = 23 bottles
Let's say that Melisande received b dollars for each bottle. The total amount she received for all the bottles is therefore:
23 bottles × b dollars/bottle = 23b dollars
Melisande also had to pay a one-time service fee of $0.25. So her total earnings after paying that fee is:
23b dollars - $0.25 = $3.20
To solve for b, we can isolate it on one side of the equation:
23b - 0.25 = 3.20
23b = 3.20 + 0.25
23b = 3.45
b = 3.45 / 23
b ≈ 0.15
Therefore, the value of b is approximately $0.15.
Judah worked at the bakery for 14 hours last week. He spent $12 of his earnings on a cake for his father’s birthday. If he was left with $86 after buying the cake, what is Judah’s hourly wage?
$6.14
$7.00
$8.00
$9.63
Let's say that Judah's hourly wage is x dollars per hour.
In 14 hours, his earnings would be:
14 hours x dollars/hour = 14x dollars
After buying the cake, his earnings would be:
14x dollars - $12 = $86
We can solve for x by isolating it on one side of the equation:
14x - 12 = 86
14x = 86 + 12
14x = 98
x = 98/14
x = 7
Therefore, Judah's hourly wage is $7 per hour.
Mr. Pham wrote the equation below on the board.
18 minus 7 x = negative 20.5
What is the value of x?
Negative 5 and one-half
Negative StartFraction 5 Over 14 EndFraction
StartFraction 5 Over 14 EndFraction
5 and one-half
To solve for x in the equation 18 - 7x = -20.5, we can use the following steps:
1. Subtract 18 from both sides of the equation:
18 - 7x - 18 = -20.5 - 18
Simplifying:
-7x = -38.5
2. To find the value of x, divide both sides of the equation by -7:
-7x / -7 = -38.5 / -7
Simplifying:
x = 5.5
Therefore, the value of x in the equation 18 - 7x = -20.5 is x = 5.5, which is equivalent to 5 and one-half.
Mr. Lopez wrote the equation 32 g + 8 g minus 10 g = 150 on the board. Four students explained how to solve for g.
Alyssa: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then subtracted 30 from 150 to find the value of g, which is 120.”
Rahul: “I added 32, 8, and 10 to get 50, and then I subtracted 150 to find the value of g, which is –100.”
Toni: “I subtracted 18 from 32 to get 14, which I then divided into 150 to find the value of g, which is 10 and StartFraction 5 Over 7 EndFraction.”
Wilhem: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then divided both sides by 30 to find the value of g, which is 5.”
Which student’s work is correct?
Alyssa
Rahul
Toni
Wilhem
To solve the equation 32g + 8g - 10g = 150 and find the value of g, we need to simplify the left side of the equation and then solve for g. Here's how to do it:
32g + 8g - 10g = 150
(32g + 8g) - 10g = 150
30g = 150
g = 150/30
g = 5
Therefore, Wilhem's work is correct, and the value of g is 5.
This is Daniela’s work to solve the equation 13 x + 42 = 276.
13 x + 42 = 276. 13 x = 318. x = 24 and StartFraction 6 Over 13 EndFraction.
Which property did Daniela need to use to avoid her error?
division property of equality
multiplication property of equality
subtraction property of equality
identity property of equality
The property that Daniela needed to use to avoid her error is the division property of equality.
After combining like terms on the left side of the equation, she correctly obtained 13x = 318. However, she made an error while solving for the value of x.
To solve for x incorrectly, Daniela multiplied both sides of the equation by 2:
13x = 318
2 * 13x = 2 * 318
26x = 636
x = 24 + 12/26
x = 24 and 6/13
In order to solve for x correctly, she should have divided both sides of the equation by 13:
13x + 42 = 276
13x = 276 - 42
13x = 234
x = 234/13
x = 18
Therefore, the property of equality that Daniela needed to use is the division property of equality.