Algebra 2 homework help please!?

Question

1. Expand (2x+3)^5

2. (X+15)/ (X+6) ≥2

Answer 1

1.The expression is (2x+3)^5

Now we use the formula

Let x = 2x, y = 3 and n = 5

Apply formula

(The values of )

(The values of )

The expansion of .

Answer 2

2). The inequality is (X+15)/ (X+6) ≥2

Multiply each side by (X + 6)

{(X+15)/ (X+6)}*(X + 6) ≥2(X + 6)

(X+15) ≥2(X+6)                                          (Simplify)

(X+15) ≥2X+12                                          (Multiply)

Subtract X from each side

X+15 - X ≥2X+12 - X

15 ≥X+12                                                   (Simplify)

Subtract 12 from each side

15 - 12 ≥X+12 - 12

3 ≥X                                                           (Simplify)

The inequality solution set is {X / X ≤ 3}.

Comments

Solution of the inequality (X+15)/ (X+6) ≥2 is  -6 < x  ≤ 3.

Answer 3

1.

(Apply bionomial theorem)

 

Answer 4

2.

(x + 15) / (x + 6) ≥ 2

(x + 6 + 9) / (x + 6) ≥ 2

(x + 6) / (x + 6) + 9 / (x + 6) ≥ 2

1 + 9 / (x + 6)≥ 2

Subtract 1 from each side

9 / (x + 6) ≥ 2 -1

9 / (x + 6) ≥ 1

Multiply each side by (x + 6)

9 ≥ (x + 6)

x + 6 ≤ 9

Subtract 6 from each side

x + 6 - 6 ≤ 9 - 6

x ≤ 3.

 

Answer 5

The inequality is

• Step-1

State the exclude values,These are the values for which denominator is zero.

The exclude value of the inequality is -6.

• Step - 2

Solve the related equation

Solution of related equation x   = 3.

• Step - 3

Draw the vertical lines at the exclude value and at the solution to separate the number line into intervals.

• Step - 4

Now test  sample values in each interval to determine whether values in the interval satisify the inequality.

Test x = -7 in (-∞, -6)

Above statement is false.

Test x = -1 in (-6, 3)

Above statement is true.

Test x = 4 in (3, ∞)

Above statement is false.

Test x = 3

Above statement is true.

The inequality is satisfied on the open intervals (-6, 3) .Moreover, because when x = 3, you can conclude that the solution set consists of all real numbers in the intervals (-6, 3] (Be sure to use a closed interval to indicate that can equal 3.)

Number line graph

Solution -6 < x  ≤ 3.