Solve and check.
a - 8 = -20
The solution is a = [ ] (Type an integer or a simplified fraction.)
To solve the equation, we can isolate the variable "a" by adding 8 to both sides:
a - 8 + 8 = -20 + 8
This simplifies to:
a = -20 + 8
a = -12
The solution is a = -12. Let's check if it's correct by substituting it back into the original equation:
-12 - 8 = -20
-20 = -20
Since both sides of the equation are equal, we can conclude that the solution a = -12 is correct.
Solve and check.
x / 6 = -8
The solution is x = [ ]
To solve the equation, we can isolate the variable "x" by multiplying both sides by 6:
6 * (x / 6) = -8 * 6
This simplifies to:
x = -48
The solution is x = -48. Let's check if it's correct by substituting it back into the original equation:
(-48) / 6 = -8
-8 = -8
Since both sides of the equation are equal, we can conclude that the solution x = -48 is correct.
Solve and check.
3/4y = 9
The solution is y = [ ] (Simplify your answer.)
To solve the equation, we can isolate the variable "y" by multiplying both sides by the reciprocal of 3/4, which is 4/3:
(4/3) * (3/4y) = (4/3) * 9
This simplifies to:
y = 12
The solution is y = 12. Let's check if it's correct by substituting it back into the original equation:
3/4(12) = 9
9 = 9
Since both sides of the equation are equal, we can conclude that the solution y = 12 is correct.
Solve the equation. Check your answer.
22 = x / 3 + 6
x = [ ] (simplify your answer)
To solve the equation, we can start by subtracting 6 from both sides:
22 - 6 = x/3
This simplifies to:
16 = x/3
To isolate x, we can multiply both sides by 3:
3 * 16 = x
This simplifies to:
48 = x
The solution is x = 48. Now let's check if it's correct by substituting it back into the original equation:
22 = 48/3 + 6
22 = 16 + 6
22 = 22
Since both sides of the equation are equal, we can conclude that the solution x = 48 is correct.
Solve the equation. Check your answer.
k - 1 / 3 = 10
k = [ ] (Type an integer or a decimal.)
To solve the equation, we can start by multiplying both sides by 3 to eliminate the fraction:
3(k - 1/3) = 3(10)
This simplifies to:
3k - 1 = 30
Next, we can add 1 to both sides:
3k - 1 + 1 = 30 + 1
This simplifies to:
3k = 31
Finally, we divide both sides by 3 to solve for k:
(3k)/3 = 31/3
This simplifies to:
k = 31/3
The solution is k = 31/3, which is a decimal value approximately equal to 10.33. Let's check if it's correct by substituting it back into the original equation:
k - 1/3 = 10
(31/3) - 1/3 = 10
30/3 = 10
10 = 10
Since both sides of the equation are equal, we can conclude that the solution k = 31/3 is correct.
that was incorrect
Apologies for the mistake. Let's solve the equation correctly.
To solve the equation, we'll need to isolate the variable k. We can start by adding 1/3 to both sides:
k - 1/3 + 1/3 = 10 + 1/3
This simplifies to:
k = 10 + 1/3
To add 10 and 1/3, we need to find a common denominator, which is 3.
k = (30/3) + (1/3)
This simplifies to:
k = 31/3
The solution is k = 31/3, which can also be written as a mixed number as 10 1/3.
Let's check if it's correct by substituting it back into the original equation:
k - 1/3 = 10
(31/3) - 1/3 = 10
30/3 = 10
10 = 10
Since both sides of the equation are equal, we can conclude that the solution k = 31/3 (or 10 1/3) is correct.
Solve the equation. Check your answer.
-3 (r + 8) = -53
r = [ ] (Simplify your answer. Type an integer or a fraction.)
To solve the equation, we can start by distributing the -3 to the terms inside the parentheses:
-3r - 3(8) = -53
This simplifies to:
-3r - 24 = -53
Next, we can add 24 to both sides to isolate the variable -3r:
-3r - 24 + 24 = -53 + 24
This simplifies to:
-3r = -29
Finally, we can divide both sides by -3 to solve for r:
(-3r)/-3 = -29/-3
This simplifies to:
r = 29/3
The solution is r = 29/3, which is a simplified fraction.
To check if it's correct, let's substitute it back into the original equation:
-3(r + 8) = -53
-3(29/3 + 8) = -53
-3((29 + 8 * 3) / 3) = -53
-3((29 + 24) / 3) = -53
-3(53 / 3) = -53
(-3 * 53) / 3 = -53
-159 / 3 = -53
-53 = -53
Since both sides of the equation are equal, we can conclude that the solution r = 29/3 is correct.
Solve the equation.
8n - (6n + 7) = 5
n = [ ] (Simplify your answer.)
To solve the equation, we can start by removing the parentheses:
8n - 6n - 7 = 5
Next, we can combine like terms:
2n - 7 = 5
To isolate the variable n, we can add 7 to both sides:
2n - 7 + 7 = 5 + 7
This simplifies to:
2n = 12
Finally, we can divide both sides by 2 to solve for n:
(2n) / 2 = 12 / 2
This simplifies to:
n = 6
The solution is n = 6.
Angie and Kenny play online video games. Angie buys 1 software package and 4 months of gameplay. Kenny buys 1 software package and 2 months of game play. Each software package costs $50. If their cost is $178, what is the cost of one month of game play?
The cost of one month of game play is $ [ ]. (Type an integer or a decimal.)
Let's denote the cost of one month of game play as "x".
According to the given information, Angie's cost is the cost of the software package plus 4 times the cost of one month of game play:
1 + 4x
Similarly, Kenny's cost is the cost of the software package plus 2 times the cost of one month of game play:
1 + 2x
Since their total cost is given as $178, we can set up the equation:
1 + 4x + 1 + 2x = 178
Combining like terms:
6x + 2 = 178
Subtracting 2 from both sides:
6x = 176
Dividing both sides by 6:
x = 176 / 6
Simplifying, we find:
x ≈ 29.33
Therefore, the cost of one month of game play is approximately $29.33.
incorrect
Apologies for the mistake. Let's solve it correctly.
Let's denote the cost of one month of game play as "x".
According to the given information, Angie's cost is the cost of the software package plus 4 times the cost of one month of game play:
50 + 4x
Similarly, Kenny's cost is the cost of the software package plus 2 times the cost of one month of game play:
50 + 2x
Since their total cost is given as $178, we can set up the equation:
(50 + 4x) + (50 + 2x) = 178
Combining like terms:
100 + 6x = 178
Subtracting 100 from both sides:
6x = 78
Dividing both sides by 6:
x = 78 / 6
Simplifying, we find:
x ≈ 13
Therefore, the cost of one month of game play is approximately $13.
Solve the equation. Check your solution.
6g + 2(- 4 + 5g) = 1 - g
g = [ ] (Type an integer or a simplified fraction.)
Let's simplify the equation step by step:
6g + 2(-4 + 5g) = 1 - g
First, distribute the 2 to -4 and 5g:
6g + (-8 + 10g) = 1 - g
Next, simplify the terms inside the parentheses:
6g - 8 + 10g = 1 - g
Combine like terms on both sides of the equation:
16g - 8 = 1 - g
Add g to both sides of the equation:
16g + g - 8 = 1 - g + g
Simplify:
17g - 8 = 1
Add 8 to both sides of the equation:
17g - 8 + 8 = 1 + 8
Simplify:
17g = 9
Divide both sides by 17 to solve for g:
g = 9/17
The solution is g = 9/17. Let's check if it's correct by substituting it back into the original equation:
6(9/17) + 2(-4 + 5(9/17)) = 1 - (9/17)
Simplify:
(54/17) + 2(-4 + 45/17) = (17/17) - (9/17)
Simplify further:
(54/17) + 2(-68/17 + 45/17) = 8/17
Simplify:
54/17 + 2(-23/17) = 8/17
Multiply the second term inside the parentheses:
54/17 + (-46/17) = 8/17
Combine like terms on the left side:
(54 - 46)/17 = 8/17
Simplify both sides:
8/17 = 8/17
Since both sides are equal, we can conclude that the solution g = 9/17 is correct.
Determine whether the equation below is an identity or whether it has no solution.
-5 (7x - 4) = -35x + 20
Choose the correct answer below.
The equation has no solution.
The equation is an identity.
The equation is an identity.
To prove this, we can simplify both sides of the equation separately:
-5(7x - 4) = -35x + 20
Distributing the -5 to the terms inside the parentheses:
-35x + 20 = -35x + 20
The equation simplifies to:
-35x + 20 = -35x + 20
Since the same expression is on both sides of the equation, the equation is an identity.
Solve the equation. Note if the equation is an identity or if it has no solution.
-2 (-c -8) = -2c - 8
Select the correct choice and fill in any answer boxes in your choice below.
c = [ ]
The equation is an identity.
The equation has no solution.
To solve the equation, let's simplify both sides separately:
-2(-c - 8) = -2c - 8
Distribute the -2 to the terms inside the parentheses:
2c + 16 = -2c - 8
Now, let's isolate the variable c by adding 2c to both sides:
2c + 2c + 16 = -2c + 2c - 8
This simplifies to:
4c + 16 = -8
Next, subtract 16 from both sides:
4c + 16 - 16 = -8 - 16
This simplifies to:
4c = -24
Finally, divide both sides by 4 to solve for c:
4c/4 = -24/4
This simplifies to:
c = -6
The solution is c = -6. To determine if the equation is an identity or has no solution, we can substitute c = -6 back into the original equation:
-2(-(-6) - 8) = -2(-6) - 8
-2(6 - 8) = 12 - 8
-2(-2) = 4
Both sides of the equation simplify to 4, which means the equation is an identity.
Solve the formula for the specified variable.
A = P + PRT for T
T = [ ]
To solve the formula A = P + PRT for T, we need to isolate the variable T.
We begin by subtracting P from both sides of the equation:
A - P = PRT
Next, divide both sides of the equation by PR:
(A - P) / (PR) = T
Therefore, the solution for T is:
T = (A - P) / (PR)
A rectangle has perimeter 80 cm and length 35 cm. What is its width?
The width is [ ] cm.
To find the width of the rectangle, we can use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2(Length + Width)
In this case, we have a perimeter of 80 cm and a length of 35 cm.
80 = 2(35 + Width)
Divide both sides by 2:
40 = 35 + Width
Subtract 35 from both sides:
40 - 35 = Width
5 = Width
Therefore, the width of the rectangle is 5 cm.
thats incorrect
Apologies for the mistake. Let's solve it correctly.
To find the width of the rectangle, we can use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2(Length + Width)
In this case, we have a perimeter of 80 cm and a length of 35 cm.
80 = 2(35 + Width)
Divide both sides by 2:
40 = 35 + Width
Next, subtract 35 from both sides:
40 - 35 = Width
5 = Width
Therefore, the width of the rectangle is 5 cm.
Solve the equation.
- 7 = 2x - 5
The solution is x = [ ]
To solve the equation, we can start by isolating the variable x.
Begin by adding 5 to both sides:
-7 + 5 = 2x - 5 + 5
This simplifies to:
-2 = 2x
Next, divide both sides by 2:
-2/2 = 2x/2
This simplifies to:
-1 = x
The solution is x = -1.