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How do you solve #abs(7x + 2)= 10#?

Answer 1

Nathan Axel

#x = 8/7 ; x = -12/7#

Absolute value is the distance of a given number from #0#. This means in the problem, #7x+2 = 10# or #7x+2=-10#

Solving both of the equations: #7x + 2 =10# #7x = 8# #x = 8/7#

#7x+2 = -10# #7x=-12# #x=-12/7#

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Answer 2

Jameson Allen

To solve the equation abs(7x + 2) = 10, you can split it into two cases:

( 7x + 2 = 10 ) when ( 7x + 2 ) is positive.
( -(7x + 2) = 10 ) when ( 7x + 2 ) is negative.

Solving for x in the first case: [ 7x + 2 = 10 ] [ 7x = 8 ] [ x = \frac{8}{7} ]

Solving for x in the second case: [ -(7x + 2) = 10 ] [ -7x - 2 = 10 ] [ -7x = 12 ] [ x = -\frac{12}{7} ]

So, the solutions are ( x = \frac{8}{7} ) and ( x = -\frac{12}{7} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.