Question

If (4x+1)/ (x+1) = 3x/2 then the value of x is:

• A. 1/2
• B. 2
• C. 1
• D. 2/3

Answer 1

Answer:

B. 2

$\frac{(4x+1)}{ (x+1)} = \frac{3x}{2}$

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

$8x+2=3x^2+3x$

$3x^2-5x-2=0$

Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a=3$, $b=-5$, and $c=-2$:

$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(3)(-2)}}{2(3)}$

$x = \frac{5 \pm \sqrt{25 + 24}}{6}$

$x = \frac{5 \pm \sqrt{49}}{6}$

$x = \frac{5 \pm 7}{6}$

This gives two possible solutions for $x$:

• $x_1 = \frac{5 + 7}{6} = \frac{12}{6} = 2$

• $x_2 = \frac{5 - 7}{6} = \frac{-2}{6} = -\frac{1}{3}$

The possible values of $x$ are $\mathbf{2}$ and $\mathbf{-\frac{1}{3}}$.