See solution below
Step-by-step explanation:
a) 5x - 7 ≤ -2
collect like terms:
5x ≤ -2 + 7
5x ≤ 5
Divide through by 5:
x ≤ 1
From the graph above, the inequality has a solution.
b) 2/3b > -8
Cross multiply:
2 > -8(3b)
2 > -24b
Divide through by -24:
Note: when we divide an inequality by a negative number, the inequality sign changes.
2/-24 < b
-1/ 12 < b
Hence, b > -1/12
Note: To make it easier to graph, I represented b with x
From the graph above, the inequality has a solution.
c) 3w - 7 - w < 2w + 4
2w - 7 < 2w + 4
collect like terms:
2w - 2w < 4 + 7
0 < 11
Note: To make it easier to graph, I represented b with x
From the graph, the solution is for all real numbers.