In English: calculate the value of x (if it exists) satisfies the equation the absolute value here if there is no value of x satisfies.give your reasons: 2[3x-8] = 10
Talking about absolute value, that is about the module. Apparently the sign "[]" module mark "| |". Let's remember what is a module: |X|=X if X>0 or X=0and |X|=-X if X<0.The module requires two solutions.
2|3x-8| = 10 divide the equation by 2.|3x-8| =5
get the two systems
1.1) 3x-8>0 or 3x-8=01.2) 3x-8=5
2.1) 3x-8<0 2.2) -3x+8=5
Solved:1.1) 3x-8>0 or 3x-8=0X>2 and 2/3 or X=2 and 2/3 ------ the first condition
1.2) 3x=13x=4 and 1/3 -------- the second condition
Solution 1: x=4 and 1/3
2.1) 3x-8<0 2.2) -3x+8=5
2.1) 3x-8<0 X<2 and 2/3 ------ the first condition
2.2) -3x=-3x=1 -------- the second condition
Solution 2: x=1.
Obyedinenie decisions system 1 and system 2.
General answer: x1=4 1/3 ; x2=1
