Question

b) 5(2x+3)(x+2)-2(5x-4)(x-1) = 75
c) 2x^2 +3(x-1)(x+1) = 5x(x+1)

Answer 1

b) 5( 2x + 3 )( x + 2 ) - 2( 5x - 4 )( x - 1 ) = 75

<=> 5( 2x² + 7x + 6 ) - 2( 5x² - 9x + 4 ) = 75

<=> 10x² + 35x + 30 - 10x² + 18x - 8 = 75

<=> 53x + 22 = 75

<=> 53x = 53

<=> x = 1

c) 2x² + 3( x - 1 )( x + 1 ) = 5x( x + 1 )

<=> 2x² + 3( x² - 1 ) = 5x² + 5x

<=> 2x² + 3x² - 3 - 5x² - 5x = 0

<=> -3 - 5x = 0

<=> -5x = 3

<=> x = -3/5

Answer 2

b, \(5\left(2x+3\right)\left(x+2\right)-2\left(5x-4\right)\left(x-1\right)=75\)

\(\Leftrightarrow10x^2+20x+15x+30-10x^2+10x+8x-8=75\)

\(\Leftrightarrow53x+22=75\Leftrightarrow x=1\)

Answer 3

c, \(2x^2+3\left(x-1\right)\left(x+1\right)=5x\left(x+1\right)\)

\(\Leftrightarrow2x^2+3x^2+3x-3x-3=5x^2+5x\)

\(\Leftrightarrow5x^2-3=5x^2+5x\Leftrightarrow x=-\frac{3}{5}\)