Solve for x-x-1-x-a- - 1A- 1- a -2B- a-1-2C- a2-2D- a-1-2

The correct option is B a 12|x + 1| = |x| + a If x ≥ 0, x + 1 = x + a ⇒ a = 1 If −1 ≤ x lt; 0, x + 1 = x + a ⇒ x=a 12 If x lt; −1, −x − 1 = −x + a ⇒ a ...

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Standard XII

Mathematics

Manipulation of inequalities

Solve for x:|...

Question

Solve for $x : | x + 1 | = | x | + a, a \neq \pm 1$

\frac{a}{2}

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\frac{a - 1}{2}

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\frac{1 - a}{2}

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\frac{a + 1}{2}

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Solution

The correct option is B $\frac{a - 1}{2}$
$| x + 1 | = | x | + a$
If $x \geq 0$ ,
$x + 1 = x + a \Rightarrow a = 1$

If $- 1 \leq x < 0$ ,
$x + 1 = - x + a$
$\Rightarrow x = \frac{a - 1}{2}$

If $x < - 1$ ,
$- x - 1 = - x + a \Rightarrow a = - 1$

Hence, $x = \frac{a - 1}{2}$

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Solve for x:|x+1|=|x|+a, a≠±1

The correct option is B a−12|x+1|=|x|+a If x≥0, x+1=x+a⇒a=1 If −1≤x<0, x+1=−x+a ⇒x=a−12 If x<−1, −x−1=−x+a⇒a=−1 Hence, x=a−12

Solve for $x : | x + 1 | = | x | + a, a \neq \pm 1$

The correct option is B $\frac{a - 1}{2}$
$| x + 1 | = | x | + a$
If $x \geq 0$ ,
$x + 1 = x + a \Rightarrow a = 1$

If $- 1 \leq x < 0$ ,
$x + 1 = - x + a$
$\Rightarrow x = \frac{a - 1}{2}$

If $x < - 1$ ,
$- x - 1 = - x + a \Rightarrow a = - 1$

Hence, $x = \frac{a - 1}{2}$