Inequality help?? 10 points?

Question

Write an inequality from the short word problems and solve.
1. The product of two consecutive odd integers is at most 256.
2. When 2 is added to the difference between six times a number and 5, the result is greater than 13 added to 5 times the number.
3. When 8 is subtracted from the sum of three times a number and 6, the result is less than 4 more than the number.
4. If six times a number is added to 9, the result is at most 3.
5. Coach Sorley neess to buy baseballs for the team. Each baseball costs $5. How many baseballs can he buy if he wants to spend at most $45?
6. Togo on vacation this summer, the 3 members of the McDonald family must save more than $1500. How much should each member save?

If anyone knows inequalities and can help with these 6 short word problems do so. Thanks alot

Answer 1

1. The product of two consecutive odd integers is at most 256.

Let the odd integer be n

And the consecutive odd integer is n + 2

The product of two consecutive odd integers is n(n + 2)

Given that product of two consecutive odd integers is at most 256

so, n(n + 2) > 256

The inequality is n(n + 2) > 256

Comments

Product of two consecutive odd integers is at most 256.

=> n(n + 2) ≤ 256

The inequality is n(n + 2) ≤ 256.

Answer 2

2. When 2 is added to the difference between six times a number and 5, the result is greater than 13 added to 5 times the number.

Let the number be x

Six times of a number = 6x

Difference between six times a number and 5 = 6x - 5

2 is added to the difference between six times a number and 5 = (6x - 5) + 2 --------(1)

Let the number be x

Five  times of a number = 5x

13 added to 5 times the number = 13 + 5x -----------(2)

2 is added to the difference between six times a number and 5, the result is greater than 13 added to 5 times the number.

(1) > (2)

=> (6x - 5) + 2 > 13 + 5x

=> 6x - 3 > 13 + 5x

Subtract 13 from each side

=> 6x - 3 - 13 > 13 + 5x -13

=> 6x - 16 >  5x

Subtract 5x from each side

=> 6x - 16 - 5x >  5x - 5x

=> x - 16 >  0

=> x  >  16

The value of the inequality is  x > 16

Answer 3

3. When 8 is subtracted from the sum of three times a number and 6, the result is less than 4 more than the number.

Let the number be x

Three times of a number = 3x

sum of three times a number and 6 = 3x + 6

8 is subtracted from the sum of three times a number and 6 = (3x + 6) - 8 --------(1)

Let the number be x

4 more than the number = x + 4 -----------(2)

8 is subtracted from the sum of three times a number and 6, the result is less than 4 more than the number.

(1) < (2)

=> (3x + 6) - 8 < x + 4

=> 3x - 2 < x + 4

Subtract x from each side

=> 3x - 2 - x < x + 4 - x

=> 2x - 2  <  4

Add 2 to each side

=> 2x - 2 + 2  <  4 + 2

=> 2x   <  4 + 2

=> 2x   <  6

Divide each side by 2

=> (2x) / 2   <  6 / 2

=> x  <  3

The value of the inequality is  x < 3

Answer 4

4. If six times a number is added to 9, the result is at most 3.

Let the number be x

Six times of a number = 6x

six times a number is added to 9 = 6x + 9 

six times a number is added to 9, the result is at most 3.

=> 6x + 9 ≥ 3

Subtract 9 from each side

=> 6x + 9 - 9 ≥ 3 - 9

=> 6x  ≥ 3 - 9

=> 6x  ≥ - 6

Divide each side by 6

=> (6x) / 6   ≥  - 6 / 6

=> x  ≥  - 1

The value of the inequality is  x  ≥  - 1

Comments

Six times a number is added to 9, the result is at most 3.

=> 6x + 9 ≤ 3

Subtract 9 from each side

=> 6x + 9 - 9 ≤ 3 - 9

=> 6x ≤ 3 - 9

=> 6x ≤ - 6

Divide each side by 6

=> (6x) / 6  ≤  - 6 / 6

=> x ≤  - 1

The inequality is  x  ≤  - 1.

Answer 5

5. Coach Sorley neess to buy baseballs for the team. Each baseball costs $5. How many baseballs can he buy if he wants to spend at most $45

Let the number of buy baseballs = x

Cost of each base ball = $5

The number of buying baseballs to any amount = 5x

he wants to spend at most $45

=> 5x ≥ 45

Divide each side by 5

=> (5x) / 5  ≥ 45 / 5

=> x ≥ 9

The buying baseballs are 9 or greater than 9.

Comments

He wants to spend at most $45

=> 5x ≤ 45

Divide each side by 5

=> (5x) / 5  ≤ 45 / 5

=> x ≤ 9

He can buy 9 or less than 9 baseballs.

Answer 6

6. Togo on vacation this summer, the 3 members of the McDonald family must save more than $1500. How much should each member save?

The each member save = x

Three members save = 3x

The 3 members of the McDonald family must save more than $1500

=> 3x > 1500

Divide each side by 3

=> (3x) / 3 > 1500 / 3

=> x > 500

The each member save is greater than $500.