Answer:
w = 1
Step-by-step explanation:
Because you have an absolute value that means that there are 2 possibilities, either (3x +4) is positive or negative.
Will work each case and that will give us the answers.
→ If (3x+4) is positive we have the equation
3w+ 4 = 6w +1 , subtract 3w from both sides
4 = 6w-3w+1, subtract 1 from both sides
4-1 = 6w-3w, combine like terms
3 = 3w , divide both sides by 3
1 = w
- check if our solution checks the equation given by substituting w with 1 :
|3*1+4| = 6*1+1 ;
7 = 7 is true so the one solution to the equation is w=1
→ If (3x+4) is negative we have the equation
-(3w+ 4) = 6w +1 , distribute the negative sign in parentheses
-3w -4 = 6w +1, add 3w and subtract 1 from both sides of the equation
-4 -1 = 6w +3w, combine like terms
-5 = 9w , divide both sides by 9
(-5/9) = w
- check if our solution checks the equation given by substituting w with -5/9 in the |3w + 4| = 6w + 1 :
|(3*(-5/9)+4| = 6(-5/9) +1;
|((-5/3)+(4*3/3)| = 6(-5/9) +1;
|(-5+12)/3| = (-10+3)/3;
7/3 = -7/3 not true so we reject as a solution
