Answer:
Explanation:
4x - 10 = 30
Add 10 to both sides to isolate the "4x" term:
4x - 10 + 10 = 30 + 10
4x = 40
Divide both sides by 4 to solve for "x":
x = 10
17 = T - 9
Add 9 to both sides to isolate the "T" term:
17 + 9 = T
T = 26
36 = c + 20
Subtract 20 from both sides to isolate the "c" term:
36 - 20 = c
c = 16
Y + 5 = 18
Subtract 5 from both sides to isolate the "Y" term:
Y + 5 - 5 = 18 - 5
Y = 13
3 = y + 12
Subtract 12 from both sides to isolate the "y" term:
3 - 12 = y
y = -9
S + 12 = 8
Subtract 12 from both sides to isolate the "S" term:
S + 12 - 12 = 8 - 12
S = -4
7 < 3 - 2x
Subtract 3 from both sides to isolate the "-2x" term:
7 - 3 < -2x
4 < -2x
Divide both sides by -2 (Note: when dividing by a negative number, the inequality sign flips):
-2 > x (or x < -2)
8(x-1) - 1 < 6x - 1
Distribute the 8 on the left side:
8x - 8 - 1 < 6x - 1
Combine like terms:
8x - 9 < 6x - 1
Subtract 6x from both sides to isolate the "8x" term:
8x - 6x - 9 < -1
2x - 9 < -1
Add 9 to both sides to isolate the "2x" term:
2x - 9 + 9 < -1 + 9
2x < 8
Divide both sides by 2 to solve for "x":
x < 4
9x + 1 > 2x - 1
Subtract 2x from both sides to isolate the "9x" term:
9x - 2x + 1 > -1
7x + 1 > -1
Subtract 1 from both sides to isolate the "7x" term:
7x + 1 - 1 > -1 - 1
7x > -2
Divide both sides by 7 to solve for "x":
x > -2/7
8y - 3y + 1 < 29
Combine like terms:
5y + 1 < 29
Subtract 1 from both sides to isolate the "5y" term:
5y + 1 - 1 < 29 - 1
5y < 28
Divide both sides by 5 to solve for "y":
y < 28/5 (or y < 5.6)
Five times the difference of a number and two is seven more than that number
Let the number be "x":
5(x - 2) = x + 7
Distribute the 5 on the left side:
5x - 10 = x + 7
Subtract "x" from both sides to isolate the "5x" term:
5x - x - 10 = 7
4x - 10 = 7
Add 10 to both sides to isolate the "4x" term:
4x - 10 + 10 = 7 + 10
4x = 17
Divide both sides by 4 to solve for "x":
x = 4.25
Twice a number decreased by four is greater than ten, what numbers satisfy this condition?
Let the number be "x":
2x - 4 > 10
Add 4 to both sides to isolate the "2x" term:
2x - 4 + 4 > 10 + 4
2x > 14
Divide both sides by 2 to solve for "x":
x > 7
Twice a number decreased by two is equivalent to that number increased by five.
Let the number be "x":
2x - 2 = x + 5
Subtract "x" from both sides to isolate the "2x" term:
2x - x - 2 = 5
x - 2 = 5
Add 2 to both sides to isolate the "x" term:
x - 2 + 2 = 5 + 2
x = 7