If -3x-4x2-7-4- solve for x-

Given equation is : |3x|=|4x^2 7|4 ⇒|4x^2 7||3x|=4 Using modulus property ⇒|4x^2 73x|=4 ⇒4x^2 73x= ± 4 Taking + sign : ⇒4x^2 73x= + 4 ⇒ 4x^2 7= nbsp; 12x ⇒ 4 ...

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Byju's Answer

Standard VIII

Mathematics

Reducing Equations to Simpler Form

If |3x|=|4x2-...

Question

$If | 3 x | = \frac{| 4 x^{2} - 7 |}{4}, solve for x.$

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Solution

Given equation is :
$| 3 x | = \frac{| 4 x^{2} - 7 |}{4}$
$\Rightarrow \frac{| 4 x^{2} - 7 |}{| 3 x |} = 4$
Using modulus property
$\Rightarrow ∣ ∣ ∣ \frac{4 x^{2} - 7}{3 x} ∣ ∣ ∣ = 4$
$\Rightarrow \frac{4 x^{2} - 7}{3 x} = \pm 4$
$Taking + sign$ :
$\Rightarrow \frac{4 x^{2} - 7}{3 x} = + 4$
$\Rightarrow 4 x^{2} - 7 = 12 x$
$\Rightarrow 4 x^{2} - 12 x - 7 = 0$
$\Rightarrow 4 x^{2} + 2 x - 14 x - 7 = 0$
$\Rightarrow 2 x (2 x + 1) - 7 (2 x + 1) = 0$
$\Rightarrow (2 x - 7) (2 x + 1) = 0$
$\Rightarrow x = \frac{7}{2} Or x = - \frac{1}{2}$
$Now, Taking - sign$ :
$\Rightarrow \frac{4 x^{2} - 7}{3 x} = - 4$
$\Rightarrow 4 x^{2} - 7 = - 12 x$
$\Rightarrow 4 x^{2} + 12 x - 7 = 0$
$\Rightarrow 4 x^{2} - 2 x + 14 x - 7 = 0$
$\Rightarrow 2 x (2 x - 1) + 7 (2 x - 1) = 0$
$\Rightarrow (2 x + 7) (2 x - 1) = 0$
$\Rightarrow x = - \frac{7}{2} Or x = \frac{1}{2}$
$So value of x = {- \frac{7}{2}, - \frac{1}{2}, \frac{1}{2}, \frac{7}{2}}$

Suggest Corrections

If |3x|=|4x2−7|4, solve for x.

$If | 3 x | = \frac{| 4 x^{2} - 7 |}{4}, solve for x.$