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Directions: Simply each expression or equation. 1) 4x - 10 = 30 2) 17 = T - 9 3) 36 = c + 20 4) Y + 5 = 18 5) 3 = y + 12 6) S + 12 = 8 7) 7 < 3 - 2x 8) 8(x-1) - 1 < 6x – 1 9) 9x + 1 > 2x – 1 xxxx4 10) 8y - 3y + 1 < 29 11) Five times the difference of a number and two is seven more than that number 12) Twice a number decreased by four is greater than ten, what numbers satisfy this condition? 13) Twice a number decreased by two is equivalent to than number increased by five.

User Mfcabrera
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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

User David Graf
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