1. Solve for x :
x + 7 = 8
2. Solve for y :
y - 3 = 2
3. Adding 7 to a number results 25. Find the number.
4. John had some candies. He gave 5 candies to his friend and now he has 18 candies. How many candies did John initially have ?
5. The sum of two numbers 22.5. If one number is 7.5, find the other number.
6. When 18 taken away from a number, the result is 30. Find the number.
7. If sum of two interior angles angles of a triangle is 120°, find the measure of the third angle.
8. In a right triangle, if one of the angles is 50°, find the measure of the third angle.
9. The perimeter of a triangle is 25 cm and sum of the lengths of two sides is 16 cm. Find the length of the third side.
10. The perimeter of an isosceles triangle is 35 cm. If the length of each of the two equal sides is 12 cm, find the length of the third side.
1. Answer :
x + 7 = 8
Subtract 7 from each side.
(x + 7) - 7 = 8 - 7
x + 7 - 7 = 1
x = 1
2. Answer :
y - 3 = 2
Add 3 to each side.
(y - 3) + 3 = 2 + 3
y - 3 + 3 = 5
y = 5
3. Answer :
Let x be the number.
x + 7 = 25
Subtract 7 from each side.
(x + 7) - 7 = 25 - 7
x + 7 - 7 = 18
x = 18
4. Answer :
Let m be the number of candies that John initially had.
m - 5 = 18
Add 5 to each side.
(m - 5) + 5 = 18 + 5
m - 5 + 5 = 23
m = 23
John initially had 23 candies.
5. Answer :
Let x be the other number.
x + 7.5 = 22.5
Subtract 7.5 from each side.
(x + 7.5) - 7.5 = 22.5 - 7.5
x + 7.5 - 7.5 = 15
x = 15
The other number is 15.
6. Answer :
Let x be the number.
x - 18 = 30
Add 18 to both sides.
(x - 18) + 18 = 30 + 18
x - 18 + 18 = 48
x = 48
The number is 48.
7. Answer :
Let x be the measure of third angle.
Sum of the three interiors angles of a triangle = 180°
x + 120° = 180°
Subtract 120° from each side.
(x + 120°) - 120° = 180° - 120°
x + 120° - 120° = 60°
x = 60°
Measure of the third angle is 60°.
8. Answer :
Let x be the measure of third angle.
Sum of the three interiors angles of a triangle = 180°
x + 90° + 50° = 180°
x + 140° = 180°
Subtract 140° from each side.
(x + 140°) - 140° = 180° - 140°
x + 140° - 140° = 40°
x = 40°
Measure of the third angle is 40°.
9. Answer :
Let x be the length of the third side.
Perimeter = 25
x + 16 = 25
Subtract 16 from each side.
(x + 16) - 16 = 25 - 16
x + 16 - 16 = 9
x = 9
Length of the third side is 9 cm.
10. Answer :
Let x be the length of third side.
Perimeter = 35
x + 12 + 12 = 35
x + 24 = 35
Subtract 24 from each side.
(x + 24) - 24 = 35 - 24
x = 11
Length of the third side is 11 cm.
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