Question

Hi can anyone help me with this question without the use of calculators please?

Answer 1

Answer:

$\frac{11}{6}$ units

Step-by-step explanation:

To find the x- intercepts let y = 0 , that is

6x² - 7x - 3 = 0 ← in standard form

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

Equate each factor to zero and solve for x

3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = - $\frac{1}{3}$

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = $\frac{3}{2}$

Find the difference of the 2 x- intercepts using absolute value

distance = | $\frac{3}{2}$ - (- $\frac{1}{3}$ ) | = | $\frac{3}{2}$ + $\frac{1}{3}$ | = | $\frac{11}{6}$ | = $\frac{11}{6}$