Algebra help please? Only 8 questions! I'm desperate!?

Question

Solve the inequality.

3 – 2a > 7
a < –2
a < 2
a > –2
a > 2

Solve the inequality.

3m ≤ 9
m ≥ 6
m ≥ 3
m ≤ –6
m ≤ 3

Select the inequality that models the problem.

The length of a rectangle is four times its width. If the area of the rectangle is less than 100 square meters, what is the greatest width of the rectangle?
4w + w < 100
4 + 4w < 100
4w < 100
4w • w < 100

Solve the inequality.

|x + 5| > 12
–7 < x < 7
–17 < x < 7
x > –17 or x < 7
x < –17 or x > 7

Which of the following is the solution set for the conjunction –6 < 4x + 2 < 6?
x <–2 or x > 1
x >–2 and x < 1
x > -3 over 2 or x < 3 over 2
x > -3 over 2 and x < 3 over 2

Which conjunction or disjunction is equivalent to |y – 5| < 14?
y – 5 < 14 or y – 5 < –14
y – 5 < 14 or y – 5 > –14
y – 5 > 14 and y – 5 < –14
y – 5 < 14 and y – 5 > –14

Solve the equation.
|x + 7| = 12
{–19, –5}
{–19, 5}
{–5, 19}
{5, 19}

Which mathematical statement corresponds to the given statement?

“An unknown number x is less than 3 but greater than –1.”
–1 < x < 3
–1 ≤ x < 3
–1 ≤ x ≤ 3
–1 < x ≤ 3

Which of the following inequalities represents a number y that is less than 4 but greater than –1?
–1 < y ≤ 4
–1 < y < 4
–1 ≤ y < 4
–1 ≤ y ≤ 4

Answer 1

2)

3m ≤ 9

Divide each side by 3.

3m/3  ≤  9/3

m  ≤  3

Solution : Option(4) is correct : m  ≤  3.

Answer 2

3)

The length of a rectangle = l

The width of a rectangle = w

The length of a rectangle is four times its width ⇒ l = 4w

The area of the rectangle ⇒ A = l•w = 4w • w

The area of the rectangle is less than 100 square meters.⇒ A < 100  ⇒  4w • w < 100

The greatest width of the rectangle can be found as

4w² < 100   ⇒ w² < 100/4 ⇒ w² < 25 ⇒ w < 5

The greatest possible width for condition w < 5 is w = 4.9999

Solution : Option(4) is correct : 4w • w < 100.

The greatest width is 4.9999.

Answer 3

4)

|x + 5| > 12

±(x + 5) > 12

-(x + 5) > 12      or      (x + 5) > 12

(- x - 5) > 12        or      (x + 5) > 12

(- x - 5 + 5) > (12 + 5)     or    (x + 5 - 5) > (12-5)

- x  > 17     or    x  > 7

- x(-1)  < 17(-1)     or    x  > 7

x  < -17     or    x  > 7

Solution : Option(4) is correct : x  < -17  or  x  > 7.

Answer 4

5)

– 6 < (4x + 2) < 6

- 6 - 2  <  (4x + 2 - 2)  <  6 - 2

- 8  <  4x  <  4

- 8/4  <  4x/4  <  4/4

- 2  <  x  < 1

- 2  <  x   and    x < 1

x > - 2   and    x < 1

Solution : Option(2) is correct Answer : x >–2 and x < 1.

Answer 5

6)

|y – 5| < 14

±( y – 5 ) < 14

( y – 5 ) < 14      or     - ( y – 5 ) < 14

Multiply each side by negative one for second inequity and flip the symbol.

( y – 5 ) < 14      or     ( y – 5 ) > - 14

Solution : Option(2) is correct : (y – 5) < 14   or   (y – 5) > -14 .

Answer 6

7)

|x + 7| = 12

±(x + 7) = 12

-(x + 7) = 12      or      (x + 7) = 12

(- x - 7) = 12      or      (x + 7) = 12

(-x-7+7) = (12+7)    or     (x+7-7) = (12-7)

- x  = 19    or     x  = 5

- x(-1)  = 19(-1)   or      x  = 5

x  = -19     or    x  = 5

x = { -19 , 5 }

Solution : Option(2) is correct Answer : x = { -19 , 5 }.

Answer 7

8)

An unknown number x is less than 3

⇒  x < 3

But unknown number x is greater than -1

⇒  x > –1  ⇒ -1 <  x

Combine solution is -1 <  x and x < 3  ⇒ -1 <  x < 3

Solution : Option(1) is correct Answer : -1 <  x < 3.

Answer 8

9)

A number y is less than 4

⇒  y < 4

But number 7 is greater than -1

⇒ y > –1  ⇒ -1 <  y

Combine solution is -1 < y  and  y < 4  ⇒ -1 <  y < 4

Solution : Option(2) is correct Answer : -1 <  y < 4.

Answer 9

1)

3 – 2a  >  7

Subtract 3 from each side.

3 - 2a - 3  >  7 - 3

- 2a  >  4

Divide each side by 2.

- 2a/(2)  >  4/2

- a  >  2

Multiply each side by negative one and flip the symbol.

-a(-1)  <  2(-1)

a < -2

Solution : Option(1) is correct Answer : a < -2.