Problem 1 :
Solve :
x + (-11) = -25
Problem 2 :
Solve :
8y = -24
Problem 3 :
-11 + y = 9
Given the above equation, find the value of
20 - (11 - y)
Problem 4 :
If 33 - x = x + 27 - 5x, what is the value of (33 + 3x)?
Problem 5 :
If (1/2)x + 3 = 3/4 - x, what is the value of x?
Problem 6 :
Solve the following equation :
x - (3 - 2x) + (4 - 5x) = -7
Problem 7 :
(4/5)(x - 5) - (1/5)(x - 10) = 19
Problem 8 :
If three quarters of a number decreased by twenty is equal to eighty two, what is that number?
Problem 9 :
There are one hundred forty-two students in a high school band. These students represent two ninth of the total students in the high school. Find the total number of students in the school.
Problem 10 :
The quotient of a number and five equals nine less than one half of the number. What is the number?
Problem 11 :
(1/3)(15 - 6x) = 5 - kx
If the linear equation above is an identity, what is the value of k?
Problem 12 :
(1/3)(9 - 6x) = 5 - kx
If the linear equation above has no solution, find the value of k.
1. Answer :
x + (-11) = -25
Add 1 to both sides.
x + (-11) + 11 = -25 + 11
x = -14
2. Answer :
8y = -24
Divide both sides by 8.
8y/8 = -24/8
y = -3
3. Answer :
-11 + y = 9
Add 11 to both sides.
y = 20
The value of 20 - (11 - y) :
20 - (11 - y) = 20 - (11 - 20)
= 20 - (-9)
= 20 + 9
= 29
4. Answer :
33 - x = x + 27 - 5x
33 - x = 27 - 4x
Add 5x to both sides.
33 + 3x = 27
Subtract 33 from both sides.
3x = -6
Divide both sides by 3.
x = -2
The value of (33 + 3x) :
33 + 3x = 33 + 3(-2)
= 33 - 6
= 27
5. Answer :
(1/2)x + 3 = 3/4 - x
Add x to both sides.
x/2 + x + 3 = 3/4
Subtract 3 from both sides.
x/2 + x = 3/4 - 3
(x + 2x)/2 = (3 - 12)/4
3x/2 = -9/4
Multiply both sides by 2.
3x = -18/4
3x = -9/2
Divide both sides by 3.
x = -9/6
x = -3/2
6. Answer :
x - (3 - 2x) + (4 - 5x) = -7
x - 3 + 2x + 4 - 5x = -7
-2x + 1 = -7
Subtract 1 from both sides.
-2x = -8
Divide both sides by -2.
x = 4
7. Answer :
(4/5)(x - 5) - (1/5)(x - 10) = 21
Multiply both sides of the equation by 5 to get rid of the denominators.
4(x - 5) - 1(x - 10) = 95
Use Distributive property.
4x - 20 - x + 10 = 95
3x - 10 = 95
Add 10 to both sides.
3x = 105
Divide both sides by 3.
x = 35
8. Answer :
Let x be the number.
(3/4)x - 20 = 82
3x/4 - 20 = 82
Add 20 to both sides.
3x/4 = 102
Multiply both sides by 4.
3x = 408
Divide both sides by 3.
x = 136
The number is 136.
9. Answer :
Let x be the total number of students in the school.
(2/9)x = 142
Multiply both sides by 9.
2x = 1278
Divide both sides by 2.
x = 639
The total number of students in the school is 639.
10. Answer :
Let x be the number.
x/5 = (1/2)x - 9
x/5 = x/2 - 9
In the equation above, we find two different denominators 5 and 2.
The least common multiple of (2, 5) is 10.
Multiply both sides of the above equation by 10 to get rid of the denominators.
10(x/5) = 10(x/2 - 9)
2x = 10x/2 - 90
2x = 5x - 90
Subtract 5x from both sides.
-3x = -90
Divide both sides.
x = 30
The number is 30.
11. Answer :
If an equation is an identity, then it will have infinitely many solution.
(1/3)(15 - 6x) = 5 - kx
Use Distributive Property.
5 - 2x = 5 - kx
Subtract 5 from both sides.
-2x = -kx
Multiply both sides by -1.
2x = kx
In the equation above, if k = 2,
2x = 2x
The above equation is true for all values of x, hence it is an identity.
So, the given equation is an identity when k = 2.
12. Answer :
(1/3)(9 - 6x) = 5 - 2x
Use Distributive Property.
3 - 2x = 5 - kx
In the equation above, if k = 2,
3 - 2x = 5 - 2x
Add 2x to both sides.
3 = 5
(false statement)
So, the given equation has no solution when k = 2.
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