-16z-19=-12z+9
To solve the equation, we need to isolate the variable, "z".
First, we want to get rid of the constants on both sides of the equation. We can do this by adding 16z to both sides:
-16z - 19 + 16z = -12z + 9 + 16z
This simplifies to:
-19 = 4z + 9
Next, we want to isolate the term with "z" by subtracting 9 from both sides:
-19 - 9 = 4z + 9 - 9
This simplifies to:
-28 = 4z
Finally, we want to solve for "z" by dividing both sides by 4:
-28/4 = 4z/4
This simplifies to:
-7 = z
Therefore, the solution to the equation is z = -7.
-2/7z+9=17
To solve the equation, we need to isolate the variable, "z".
First, let's get rid of the constant on the left side of the equation. We can do this by subtracting 9 from both sides:
-2/7z + 9 - 9 = 17 - 9
Simplifying, we have:
-2/7z = 8
Next, we want to isolate the variable z. We do this by multiplying both sides by the reciprocal of -2/7, which is -7/2:
(-2/7z)(-7/2) = 8(-7/2)
Simplifying the left side, we have:
z = -56/2
Simplifying the right side, we have:
z = -28
Therefore, the solution to the equation is z = -28.
a movie theater offers two options for membership. the first option costs $15 but an initial fee of $10. the second option costs $10 per ticket but an initial fee of $45. After how many tickets are both options the same price?
Let's assume "x" represents the number of tickets purchased.
For the first option, the total cost is given by $15 + $10x.
For the second option, the total cost is given by $10x + $45.
To find when both options are the same price, we can set the two expressions equal to each other and solve for x:
$15 + $10x = $10x + $45
Let's cancel out the terms with the variable by subtracting $10x from both sides:
$15 = $45
This equation is not possible since $15 cannot be equal to $45.
Therefore, there is no number of tickets where both options are the same price.
To vats are being filled by two different pumps. The first that has 10 gallons is being filled at a rate of 12 gallons per second. The second that has 25 gallons and is being filled at a rate of 10 gallons per second. After how many seconds will both bats have the same amount of liquid?
Let's assume "t" represents the number of seconds needed for both vats to have the same amount of liquid.
For the first vat, the amount of liquid at time "t" can be represented as 10 + 12t (10 gallons plus the rate of 12 gallons per second).
For the second vat, the amount of liquid at time "t" can be represented as 25 + 10t (25 gallons plus the rate of 10 gallons per second).
To find when both vats have the same amount of liquid, we can set the two expressions equal to each other and solve for t:
10 + 12t = 25 + 10t
Let's subtract 10t from both sides to isolate the "t" term:
10 - 25 = 10t - 12t
Simplifying:
-15 = -2t
Now, divide both sides by -2 to solve for "t" alone:
-15 / -2 = -2t / -2
Simplifying:
7.5 = t
Therefore, after 7.5 seconds, both vats will have the same amount of liquid.
2 (24x + 7) = 39x +___x + 14
To solve the equation, let's distribute the 2 on the left side:
2 * 24x + 2 * 7 = 39x + ___x + 14
This simplifies to:
48x + 14 = 39x + ___x + 14
Next, we can combine like terms on the right side:
48x + 14 = 39x + ___x + 14
We are missing the coefficient of "x" in the equation, so we can't solve it without that information. Please provide the missing coefficient of "x" so we can proceed further with solving the equation.