Question

Please please help me!!

Answer 1

x= -1/3 & -2/3

Explanation:

1=(2x+1)(3x+4)

1=6x^2+11x+4

0=6x^2+11x+3

(3x+1)(2x+3)=0

therefore, x= -1/3 & -2/3

Answer 2

x = -
`(1)/(3)` & -
`(3)/(2)`

Explanation:

`(1)/(2x+1)` = 3x + 4 ( x ≠ -
`(1)/(2)` )

multiply through by 2x + 1 to clear the fraction

1 = 3x(2x + 1) + 4(2x + 1) ← distribute parenthesis

1 = 6x² + 3x + 8x + 4 ← collect like terms

1 = 6x² + 11x + 4 ( subtract 1 from both sides )

0 = 6x² + 11x + 3 , that is

6x² + 11x + 3 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × 3 = 18 and sum = + 11

the factors are + 2 and + 9

use these factors to split the x- term

6x² + 2x + 9x + 3 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 1) + 3(3x + 1) = 0 ← factor out (3x + 1) from each term

(3x + 1)(2x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

3x + 1 = 0 ( subtract 1 from both sides )

3x = - 1 ( divide both sides by 3 )

x = -
`(1)/(3)`

and

2x + 3 = 0 ( subtract 3 from both sides )

2x = - 3 ( divide both sides by 2 )

x = -
`(3)/(2)`

solutions are x = -
`(1)/(3)` & -
`(3)/(2)`