Question

DE bisects AB at C. If AC = 2x - 1 and AB = 3x + 2, find x.

Answer 1

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

DE bisects AB at C. If AC = 2x - 1 and AB = 3x + 2, find x.

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

We know that,

• DE bisects AB at C.
• So, AC + CB = AB (C becomes the mid-point of AB).
• We can also see that, AB = BC, so 2AC = AB

Now, find the value of x.

For this, we need to use the equation ⇨ 2AC = AB.

__________

2AC = AB

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

4x - 2 = 3x + 2

4x - 3x = 2 + 2

$\boxed{\underline{\bf \: x = 4}}$

• The value of x is 4.

Answer 2

$\\ \ast\sf\hookrightarrow AB=2AC$

$\\ \ast\sf\hookrightarrow 3x+2=2(2x-1)$

$\\ \ast\sf\hookrightarrow 3x+2=4x-2$

$\\ \ast\sf\hookrightarrow 4x-3x=2+2$

$\\ \ast\sf\hookrightarrow x=4$