Question

Which of the following are the solutions to |5x + 2|=8

Answer 1

Hi there!

Let's solve this equation step by step!
$|5x + 2| = 8$

First work out the absolute value, which makes everything between the stripes positive. When we have a negative outcome between the stripes (for instance -8), the stripes make it positive. When we work out the absolute value, we mustn't forget this solution.

$5x + 2 = 8 \: \: or \: \: 5x + 2 = - 8$
Subtract 2

$5x = 6 \: \: or \: \: 5x = - 10$
Divide both sides by 5.

$x = \frac{ 6}{5} = 1 \frac{1}{5}\: \: or \: \: x = -2$
~ Hope this helps you!

Answer 2

Hi there!

| 5x + $2$ | = 8

• Absolute Value :-

The Absolute Value or Modulus | X | of a real number x is the non-negative value of x without regard to its sign.

Which makes the above Eqn's right hand side + ve in both cases.

Then,
Isolatin' the Absolute Value :-

→ For + ve value :

=> 5x + 2 = 8

=> 5x = 8 - 2

=> 5x = 6

=> x = $\dfrac {6}{5}$

→ For - ve value :

=> 5x + 2 = -8

=> 5x = - 8 - 2

=> 5x = - 10

=> x = $\dfrac {- 10}{5}$ = -2

Hence,
Solution for the Eqn. are :-

=> x = -2 Or => x = $\dfrac {6}{5}$

~ Hope it helps!