What are the possible values of x- satisfying the equation -4 x-6-2-2 x-3 -A- -5-2 andB- -5-2 and -6-7C- 5-2 and 6-7 D- -5-2 and -7-6

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Standard XII

Mathematics

Manipulating absolute value equations

What are the ...

Question

What are the possible values of x, satisfying the equation
$| 4 x + 6 | + 2 = 2 x + 3$ ?

- \frac{5}{2}

and

\frac{7}{6}

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\frac{5}{2}

and

\frac{6}{7}

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- \frac{5}{2}

and

- \frac{6}{7}

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- \frac{5}{2}

and

\frac{- 7}{6}

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Solution

The correct option is D $- \frac{5}{2}$ and $\frac{- 7}{6}$
Step 1 : Keep Absolute value expression on one side and rest of the terms on the other side of the equation.

$| 4 x + 6 | + 2 = 2 x + 3$
$| 4 x + 6 | = 2 x + 1$

Step 2 : Open the Modulus :
When, we open the mod , we get two different equations
$\begin{matrix} 4 x + 6 = 2 x + 1 & 4 x + 6 = - (2 x + 1) \end{matrix}$
Now, solve each equation, to get a value of x
$\begin{matrix} 4 x + 6 = 2 x + 1 & 4 x + 6 = - (2 x + 1) 2 x = - 5 & 4 x + 6 = - 2 x - 1 X = - \frac{5}{2} & 6 x = - 7 X = - \frac{7}{6} \end{matrix}$

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Similar questions

Question 6

Which of the following expressions show that rational numbers are associative under multiplication.
(a) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5}$
(b) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = \frac{2}{3} \times (\frac{3}{5} \times \frac{- 6}{7})$
(c) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{3}{5} \times \frac{2}{3}) \times \frac{- 6}{7}$
(d) $(\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5} = (\frac{- 6}{7} \times \frac{2}{3}) \times \frac{3}{5}$

Question 6

What values of $x$ satisfy the given equation
$x^{2} - 3 x - 10 = 0$ ?

Q. Solution of

| x + 2 | + | 2 x + 6 | + | 3 x - 3 | = 12

Q. The total possible no. of roots of the equation

4 x^{7} + 3 x^{6} + 2 x^{5} + 9 x^{4} + 4 x^{3} + x^{2} + 9 x + 9 = 0

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What are the possible values of x, satisfying the equation |4x+6|+2=2x+3?

What are the possible values of x, satisfying the equation
$| 4 x + 6 | + 2 = 2 x + 3$ ?