Question 1203651
<br>
The solutions shown by the other tutors are good formal mathematical solutions.<br>
A different method for solving absolute value problems like this is to interpret<br>
{{{abs(x-a)<b}}}<br>
as<br>
"x is less than b units from a"<br>
Applying that method to this problem....<br>
{{{4abs(2x+3)-7<9}}}
{{{4abs(2x+3)<16}}}
{{{abs(2x+3)<4}}}
{{{abs(x+1.5)<2}}}
{{{abs(x-(-1.5))<2}}}<br>
This says that x is less than 2 units from -1.5.<br>
2 units to the left of -1.5 is -3.5; 2 units to the right of -1.5 is 0.5.  So the solution is<br>
-3.5 < x < 0.5<br>