To solve the inequality 7.82x + 1.83 < 15.42, we can isolate the variable x by performing the following steps:
1. Subtract 1.83 from both sides of the inequality:
7.82x + 1.83 - 1.83 < 15.42 - 1.83
7.82x < 13.59
2. Divide both sides of the inequality by 7.82 to solve for x:
(7.82x)/7.82 < 13.59/7.82
x < 1.7381
Rounded to the nearest hundredth, the solution for x is x < 1.74.