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This is one of our many quizzes on Absolute value. Click on this to access more such competitive quizzes on Number System.

Absolute value Quiz 2

mathematics

 Solve $\left| {3x - 4} \right| = \left| {5x - 6} \right|$and choose the correct option.

 Apply the property $\left| a \right| = \left| b \right|$ which has the following four solutions $a = b$, $a =  - b$ , $ - a =  - b$ , $ - a = b$.

 Apply the property $\left| a \right| = \left| b \right|$ we have the following four solutions:  $ \\ $ $a = b$, $a =  - b$ , $ - a =  - b$ , $ - a = b$. $ \\ $ Then $3x - 4 = 5x - 6$ , $3x - 4 =  - (5x - 6)$ , $- (3x - 4) =  - (5x - 6)$ , $- (3x - 4) = 5x - 6$. $ \\ $ On solving equation $1$ and equation two. $ \\ 3x - 4 = 5x - 6 \\ \Rightarrow  - 2x =  - 2 \\ \Rightarrow x = 1 \\ $ On solving equation $2$ we get, $ \\  3x - 4 =  - (5x - 6) \\  \Rightarrow 8x = 10 \\ \Rightarrow x = \dfrac{{10}}{8} = \dfrac{5}{4} $

 State the correct answer for the question $\left| {\dfrac{{5x - 1}}{3}} \right| = \dfrac{7}{6}$.

 Apply the absolute modulus property of $\left| { \pm a} \right| = a$.

 Apply the property of modulus $\left| { \pm a} \right| = a$. $ \\ $ $ \dfrac{{5x - 1}}{3} =  - \dfrac{7}{6}$ and $\dfrac{{5x - 1}}{3} = \dfrac{7}{6}$ $ \\ $ On solving equation one we get, $ \\ \dfrac{{5x - 1}}{3} =  - \dfrac{7}{6} \\ \Rightarrow 30x - 6 =  - 21 \\ \Rightarrow x = \dfrac{{ - 15}}{{30}} =  - \dfrac{1}{2} \\ $ On solving equation two we get, $ \\ \dfrac{{5x - 1}}{3} = \dfrac{7}{6} \\  \Rightarrow 30x - 6 = 21 \\   \Rightarrow 30x =  27 \\ \Rightarrow x = \dfrac{9}{{10}}$

 Solve the question $3\left| {3x - 6} \right| = 9$ and select the correct answer.

 First simplify the modulus part such that you have only the modulus part on the left hand side. Do not multiply $2$ inside the modulus.

 $3\left| {3x - 6} \right| = 9 \\  \Rightarrow \left| {3x - 6} \right| = \dfrac{9}{3} \\ \Rightarrow \left| {3x - 6} \right| = 3 \\ $ Applying the property $\left| { \pm a} \right| = a$. We get two equations: $3x - 6 = 3$ and $3x - 6 =  - 3$. $ \\ $ On solving equation one we get, $ \\ 3x - 6 = 3 \\ \Rightarrow x = 3 \\ $ On solving equation two we get, $ \\ 3x - 6 =  - 3 \\ \Rightarrow x = 1$

 Mark the correct option for $4\left| {3(x - 3)} \right| = 12$

 Initially simplify the given question such that we have the modulus part only at one side completely. Do not multiply $4$ inside the modulus. 

 $4\left| {3(x - 3)} \right| = 12 \\   \Rightarrow \left| {3(x - 3)} \right| = 3 \\   \Rightarrow \left| {3x - 9} \right| = 3 \\ $ On applying the property $\left| { \pm a} \right| = a$ we get: $3x - 9 = 3$ and $3x - 9 =  - 3$. $ \\ $ On solving equation one we get, $ \\ 3x - 9 = 3 \\ \Rightarrow x = 4 \\ $ On solving equation two we get, $ \\ 3x - 9 =  - 3 \\ \Rightarrow x = 2 $

 Select the correct answer for the question $5\left| {3(2x + 3)} \right| + 9 = 15$

 Firstly simplify the given question such that we have the modulus part only at one side completely. 

 $ 5\left| {3(2x + 3)} \right| + 9 = 15 \\  \Rightarrow 5\left| {3(2x + 3)} \right| = 6 \\ \Rightarrow \left| {6x + 9} \right| = \dfrac{6}{5} \\ $ On applying the property $\left| { \pm a} \right| = a$ we get: $6x + 9 = \dfrac{6}{5}$ and $6x + 9 =  - \dfrac{6}{5}$ $ \\ $ On solving equation one we get,  $ \\ 6x + 9 = \dfrac{6}{5} \\ \Rightarrow 35x + 45 = 6 \\  \Rightarrow 35x =  - 39 \\ \Rightarrow x =  - \dfrac{{39}}{{35}} \\ $ On solving equation two we get, $ \\  6x + 9 =  - \dfrac{6}{5} \\   \Rightarrow 35x + 45 =  - 6 \\   \Rightarrow 35x =  - 51 \\   \Rightarrow x =  - \dfrac{{51}}{{35}} \\  $