Combining like terms on the left side of the equation, we have:
2x + 8x + 19 + 9 = -102
Combining the x terms and the constant terms, we have:
10x + 28 = -102
Next, we isolate the x term by subtracting 28 from both sides:
10x = -102 - 28
10x = -130
Finally, we solve for x by dividing both sides by 10:
x = -130/10
x = -13
2x+19+8x+9=-102
x=?
9 answers
-16z-19=-12z+9
z=?
z=?
To solve for z, start by combining like terms:
-16z - 19 = -12z + 9
Add 12z to both sides:
-4z - 19 = 9
Add 19 to both sides:
-4z = 28
Finally, divide both sides by -4:
z = -28/4
z = -7
-16z - 19 = -12z + 9
Add 12z to both sides:
-4z - 19 = 9
Add 19 to both sides:
-4z = 28
Finally, divide both sides by -4:
z = -28/4
z = -7
-2/7z+9=17
z=?
z=?
To solve for z, start by isolating the variable term by subtracting 9 from both sides of the equation:
-2/7z = 17 -9
Simplify:
-2/7z = 8
Next, multiply both sides of the equation by the reciprocal of -2/7, which is -7/2:
(z) = 8*(-7/2)
Simplify:
z = -56/2
Finally, simplify the fraction:
z = -28
-2/7z = 17 -9
Simplify:
-2/7z = 8
Next, multiply both sides of the equation by the reciprocal of -2/7, which is -7/2:
(z) = 8*(-7/2)
Simplify:
z = -56/2
Finally, simplify the fraction:
z = -28
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 $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: 15x + 10.
For the second option, the total cost is given by: 10x + 45.
To find the number of tickets where both options have the same price, we set the two expressions equal to each other and solve for x:
15x + 10 = 10x + 45
Subtract 10x from both sides:
5x + 10 = 45
Subtract 10 from both sides:
5x = 35
Divide both sides by 5:
x = 7
Therefore, after purchasing 7 tickets, both options would have the same price.
For the first option, the total cost is given by: 15x + 10.
For the second option, the total cost is given by: 10x + 45.
To find the number of tickets where both options have the same price, we set the two expressions equal to each other and solve for x:
15x + 10 = 10x + 45
Subtract 10x from both sides:
5x + 10 = 45
Subtract 10 from both sides:
5x = 35
Divide both sides by 5:
x = 7
Therefore, after purchasing 7 tickets, both options would have the same price.
Two vats are being filled by two different pumps. The first vat has 10 gallons and is being filled at a rate of 12 gallons per second. The second vat has 25 gallons and is being filled at a rate of 10 gallons per second. After how many seconds will both vats have the same amount of liquid??
Let's represent the number of seconds it takes for both vats to have the same amount of liquid as 't'.
The total amount of liquid in the first vat after 't' seconds is given by: 10 + 12t.
The total amount of liquid in the second vat after 't' seconds is given by: 25 + 10t.
Setting these two expressions equal to each other, we have:
10 + 12t = 25 + 10t
Subtracting 10t from both sides:
2t = 15
Dividing both sides by 2:
t = 7.5
Therefore, it will take 7.5 seconds for both vats to have the same amount of liquid.
The total amount of liquid in the first vat after 't' seconds is given by: 10 + 12t.
The total amount of liquid in the second vat after 't' seconds is given by: 25 + 10t.
Setting these two expressions equal to each other, we have:
10 + 12t = 25 + 10t
Subtracting 10t from both sides:
2t = 15
Dividing both sides by 2:
t = 7.5
Therefore, it will take 7.5 seconds for both vats to have the same amount of liquid.