How do you solve the equation #abs(3x-1)=10#?

1 Answer
Mar 22, 2017

Answer:

Please see the explanation.

Explanation:

Use #|a| ={ (a; a>=0), (-a; a <0) :}#

Substitute #3x-1# for a:

#3x -1 = 10; 3x-1>=0 and -(3x-1) = 10; 3x-1<0#

Simplify the inequalities:

#3x -1 = 10; x>=1/3 and -(3x-1) = 10; x<1/3#

Solve the equations:

#3x -1 = 10; x>=1/3 and 3x-1 = -10; x<1/3#

#3x = 11; x>=1/3 and 3x = -9; x<1/3#

#x = 11/3; x>=1/3 and x = -3; x<1/3#

The equations do not violate the inequalities, therefore, both are equations are true:

#x = 11/3 and x = -3#

Check:

#|3(11/3)-1| = 10#
#|3(-3)-1| = 10#

#|11-1| = 10#
#|-9-1| = 10#

#|10| = 10#
#|-10| = 10#

#10 = 10#
#10 = 10#

This checks.