Question

if |7x-19|>(or)=3 then x​

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:x\:\geq\:\dfrac{22}{7}}}\sf\:\quad\:OR\:\quad\:\boxed{\red{\sf\:x\:\leq\:\dfrac{16}{7}}}}$

Step-by-step-explanation:

The given inequality is

$\displaystyle{\sf\:|\:7x\:-\:19\:|\:\geq\:3}$

We have to find the value of x.

Now,

$\displaystyle{\sf\:|\:7x\:-\:19\:|\:\geq\:3}$

$\displaystyle{\implies\sf\:7x\:-\:19\:\geq\:3\:\quad\:OR\:\quad\:7x\:-\:19\:\leq\:-\:3}$

$\displaystyle{\implies\sf\:7x\:\geq\:3\:+\:19\:\quad\:OR\:\quad\:7x\:\leq\:-\:3\:+\:19}$

$\displaystyle{\implies\sf\:7x\:\geq\:22\:\quad\:OR\:\quad\:7x\:\leq\:16}$

$\displaystyle{\implies\:\underline{\boxed{\red{\sf\:x\:\geq\:\dfrac{22}{7}}}}\sf\:\quad\:OR\:\quad\:\underline{\boxed{\red{\sf\:x\:\leq\:\dfrac{16}{7}}}}}$

$\displaystyle{\therefore\:\boxed{\blue{\sf\:\dfrac{16}{7}\:\geq\:x\:\geq\:\dfrac{22}{7}\:}}}$

The solution set in interval notation can be written as

$\displaystyle{\boxed{\pink{\sf\:x\:\in\:\left(\:-\:\infty\:,\:\dfrac{16}{7}\:\right]\:\cup\:\left[\:\dfrac{22}{7}\:,\:\infty\:\right)\:}}}$

Answer 2

Step-by-step explanation:

The solution set in interval notation can be written as