How do you solve and graph the compound inequality #3x>=5# or #-5/8x-6>1# ?

graph{x>=5/3 [-10, 10, -5, 5]}

graph{x<-7/58 [-10, 10, -5, 5]}

=========|-56/5 -----------------|0-----|5/3=============

NOTE. The end (critical) point (5/3) is included in the solution set.

To solve and graph the compound inequality 3x ≥ 5 or -5/8x - 6 > 1:

1. Solve each inequality separately. For 3x ≥ 5: 3x ≥ 5 x ≥ 5/3

   For -5/8x - 6 > 1: -5/8x - 6 > 1 -5/8x > 1 + 6 -5/8x > 7 Multiply both sides by -8/5 (since multiplying or dividing by a negative number reverses the inequality) x < -56/8 x < -7

2. Combine the solutions using the 'or' statement, which means the solution set includes all values that satisfy either inequality.

   Solution: x ≥ 5/3 or x < -7

3. Graph the solution set on the number line.

   • Start by marking the critical points, which are 5/3 and -7.
   • For the inequality x ≥ 5/3, draw a solid dot at 5/3 and shade to the right since it's "greater than or equal to."
   • For the inequality x < -7, draw an open dot at -7 and shade to the left since it's "less than."