Question

Algebra please help!

Answer 1

1. x = -2

2. (7x + 4)/(x² - x - 56)

3. 12

4. x = 84

Explanation:

1. sqrt(3 - 2x) = sqrt(1 - 3x)

3 - 2x = 1 - 3x

x = -2

Check:

sqrt(3 - 2(-2)) = sqrt(1 - 3(-2))

sqrt(7) = sqrt(7)

2. [3(x - 8) + 4(x + 7)]/[(x + 7)(x - 8)]

[3x - 24 + 4x + 28]/(x² + 7x - 8x - 56)

(7x + 4)/(x² - x - 56)

3. 4P2

4!/2!

4×3×2!/2!

12

4. -6log3(x - 3) = -24

log3(x - 3) = 4

x - 3 = 3⁴

x - 3 = 81

x = 84

Answer 2

1. x= -2

2. -52

3. 12

4 x = 84

Explanation:

sqrt( 3-2x) = sqrt( 1-3x)

Square each side

(sqrt( 3-2x))^2 = (sqrt( 1-3x))^2

3-2x = 1-3x

Add 3x to each side

3-2x+3x = 1-3x+3x

3+x = 1

Subtract 3 from each side

3+x-3 =1-3

x = -2

Check

sqrt( 3-2(-2)) = sqrt( 1-3(-2))

sqrt(3+4) = sqrt(1+6)

sqrt(7) = sqrt(7)

3/(x+7) = 4/(x-8)

Using cross products

3(x-8) = 4(x+7)

Distribute

3x-24 = 4x+28

Subtract 3x from each side

3x-3x-24 = 4x-3x+28

-24 = x+28

Subtract 28 from each side

-24 -28 =x+28-28

-52 =x

permutation notation P(n,r) = nPr = n!/(n-r)!

4P2 = 4!/ (4-2)! = 4*3*2*1/ 2*1 = 12

-6 log3 (x-3) = -24

Divide each side by -6

-6/-6 log3 (x-3) = -24/-6

log3( x-3) = 4

Raise each side to the base of 3

3 ^ log3( x-3) =3^ 4

x-3 = 81

Add 3 to each side

x-3+3 = 81+3

x = 84