To solve for z, we need to isolate it on one side of the equation.
Starting with the equation −2z + 4 = 19, we can begin by subtracting 4 from both sides:
−2z + 4 - 4 = 19 - 4
−2z = 15
Next, divide both sides of the equation by -2:
−2z/-2 = 15/-2
z = -7.5
Therefore, the solution to the equation −2z + 4 = 19 is z = -7.5.
−2z+4=19
11 answers
4(x−6)=9
To solve for x, we need to isolate it on one side of the equation.
Starting with the equation 4(x - 6) = 9, we can begin by distributing the 4 to the terms inside the parentheses:
4x - 24 = 9
Next, we can add 24 to both sides of the equation to move the constant term to the right side:
4x - 24 + 24 = 9 + 24
4x = 33
Finally, divide both sides of the equation by 4 to solve for x:
4x/4 = 33/4
x = 33/4
Therefore, the solution to the equation 4(x - 6) = 9 is x = 33/4.
Starting with the equation 4(x - 6) = 9, we can begin by distributing the 4 to the terms inside the parentheses:
4x - 24 = 9
Next, we can add 24 to both sides of the equation to move the constant term to the right side:
4x - 24 + 24 = 9 + 24
4x = 33
Finally, divide both sides of the equation by 4 to solve for x:
4x/4 = 33/4
x = 33/4
Therefore, the solution to the equation 4(x - 6) = 9 is x = 33/4.
−2(7x+11)=15
To solve for x, we need to isolate it on one side of the equation.
Starting with the equation −2(7x + 11) = 15, we can simplify the left side by distributing the -2 to the terms inside the parentheses:
-14x - 22 = 15
Next, we can add 22 to both sides of the equation to move the constant term to the right side:
-14x - 22 + 22 = 15 + 22
-14x = 37
Finally, divide both sides of the equation by -14 to solve for x:
-14x / -14 = 37 / -14
x = -37/14
Therefore, the solution to the equation −2(7x + 11) = 15 is x = -37/14.
Starting with the equation −2(7x + 11) = 15, we can simplify the left side by distributing the -2 to the terms inside the parentheses:
-14x - 22 = 15
Next, we can add 22 to both sides of the equation to move the constant term to the right side:
-14x - 22 + 22 = 15 + 22
-14x = 37
Finally, divide both sides of the equation by -14 to solve for x:
-14x / -14 = 37 / -14
x = -37/14
Therefore, the solution to the equation −2(7x + 11) = 15 is x = -37/14.
10y+19−2y=−125
To solve for y, we need to isolate it on one side of the equation.
Starting with the equation 10y + 19 - 2y = -125, we can simplify the left side of the equation by combining like terms:
10y - 2y + 19 = -125
This simplifies to:
8y + 19 = -125
Next, we can subtract 19 from both sides to move the constant term to the right side:
8y + 19 - 19 = -125 - 19
8y = -144
Finally, divide both sides of the equation by 8 to solve for y:
(8y) / 8 = (-144) / 8
y = -18
Therefore, the solution to the equation 10y + 19 - 2y = -125 is y = -18.
Starting with the equation 10y + 19 - 2y = -125, we can simplify the left side of the equation by combining like terms:
10y - 2y + 19 = -125
This simplifies to:
8y + 19 = -125
Next, we can subtract 19 from both sides to move the constant term to the right side:
8y + 19 - 19 = -125 - 19
8y = -144
Finally, divide both sides of the equation by 8 to solve for y:
(8y) / 8 = (-144) / 8
y = -18
Therefore, the solution to the equation 10y + 19 - 2y = -125 is y = -18.
A movie theater offers two options for membership. The first option costs $15 per ticket but an initial fee of $10. The second option costs $12.50 per ticket but an initial fee of $40 . After how many tickets are both options the same price?
____ tickets
____ tickets
Let's represent the number of tickets as "x".
For the first option, the cost is $15 per ticket plus an initial fee of $10. The total cost will be (15x + 10).
For the second option, the cost is $12.50 per ticket plus an initial fee of $40. The total cost will be (12.50x + 40).
To find out when both options are the same price, we need to set up an equation and solve for x:
15x + 10 = 12.50x + 40
Subtracting 12.50x from both sides:
15x - 12.50x + 10 = 12.50x - 12.50x + 40
2.5x + 10 = 40
Subtracting 10 from both sides:
2.5x + 10 - 10 = 40 - 10
2.5x = 30
Dividing both sides by 2.5 to solve for x:
(2.5x) / 2.5 = 30 / 2.5
x = 12
Therefore, after purchasing 12 tickets, both options will be the same price
For the first option, the cost is $15 per ticket plus an initial fee of $10. The total cost will be (15x + 10).
For the second option, the cost is $12.50 per ticket plus an initial fee of $40. The total cost will be (12.50x + 40).
To find out when both options are the same price, we need to set up an equation and solve for x:
15x + 10 = 12.50x + 40
Subtracting 12.50x from both sides:
15x - 12.50x + 10 = 12.50x - 12.50x + 40
2.5x + 10 = 40
Subtracting 10 from both sides:
2.5x + 10 - 10 = 40 - 10
2.5x = 30
Dividing both sides by 2.5 to solve for x:
(2.5x) / 2.5 = 30 / 2.5
x = 12
Therefore, after purchasing 12 tickets, both options will be the same price
There are two different vats. The first vat has 12 gallons is being filled at a rate of 3 gallons per minute. The second vat has 120 gallons and is leaking fluid at a rate of 7 gallons per minute. After how many seconds will both vats have the same amount of liquid?
____ minutes
____ minutes
Let's represent the number of minutes as "m".
For the first vat, it is being filled at a rate of 3 gallons per minute. The total amount of liquid in the first vat can be represented as 12 + 3m.
For the second vat, it is leaking fluid at a rate of 7 gallons per minute. The total amount of liquid in the second vat can be represented as 120 - 7m.
To find out when both vats have the same amount of liquid, we need to set up an equation and solve for m:
12 + 3m = 120 - 7m
Adding 7m to both sides:
12 + 3m + 7m = 120 - 7m + 7m
10m + 12 = 120
Subtracting 12 from both sides:
10m + 12 - 12 = 120 - 12
10m = 108
Dividing both sides by 10 to solve for m:
(10m) / 10 = 108 / 10
m = 10.8
Therefore, after 10.8 minutes, both vats will have the same amount of liquid.
To convert this to seconds, we multiply by 60:
10.8 minutes * 60 seconds/minute = 648 seconds
Therefore, after 648 seconds, both vats will have the same amount of liquid.
For the first vat, it is being filled at a rate of 3 gallons per minute. The total amount of liquid in the first vat can be represented as 12 + 3m.
For the second vat, it is leaking fluid at a rate of 7 gallons per minute. The total amount of liquid in the second vat can be represented as 120 - 7m.
To find out when both vats have the same amount of liquid, we need to set up an equation and solve for m:
12 + 3m = 120 - 7m
Adding 7m to both sides:
12 + 3m + 7m = 120 - 7m + 7m
10m + 12 = 120
Subtracting 12 from both sides:
10m + 12 - 12 = 120 - 12
10m = 108
Dividing both sides by 10 to solve for m:
(10m) / 10 = 108 / 10
m = 10.8
Therefore, after 10.8 minutes, both vats will have the same amount of liquid.
To convert this to seconds, we multiply by 60:
10.8 minutes * 60 seconds/minute = 648 seconds
Therefore, after 648 seconds, both vats will have the same amount of liquid.