Solve the inequality. Graph the solution set and write it in interval notation.
1/5(x+5)<1/6(3x+4)
To solve the inequality, we will first simplify both sides:
1/5(x+5) < 1/6(3x+4)
Multiply both sides by the least common denominator, which is 30:
6(x+5) < 5(3x+4)
6x + 30 < 15x + 20
Subtract 6x and 20 from both sides to isolate the variable x:
6x - 6x + 30 - 20 < 15x - 6x + 20 - 20
30 - 20 < 9x
10 < 9x
Divide both sides by 9 (remembering to flip the inequality symbol since we are dividing by a negative number, 9):
10/9 > x
x < 10/9
Therefore, the solution set for the inequality is x < 10/9. In interval notation, this can be written as (-∞, 10/9).
To graph the solution set on a number line, plot an open circle at 10/9 and shade the line to the left of that point since x is less than 10/9.