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The given expression is : 4b + 18 ≤ -12b - 14 ≤ 14 - 5b
to simplify the expression for b :
4b + 18 ≤ -12b - 14 ≤ 14 - 5b
First simplify the first two part and then last two parts :
4b + 18 ≤ -12b - 14
Add 12b on both side :
4b + 12b +18 ≤ -12b - 14 +12b
16b +18 ≤ -14
Subtract 18 on both side :
16b + 18 - 18 ≤ -14 - 18
16b ≤ -32
Divide both side by 16
16b/16 ≤ -32/16
b ≤ - 2
-12b - 14 ≤ 14 - 5b
Add 12b on both side :
-12b - 14 + 12b ≤ 14 - 5b + 12b
-14 ≤ 14 +7b
Add 14 on both side :
-14 + 14 ≤ 14 +7b + 14
0 ≤ 28 +7b
Subtract 28 on both side :
0 - 28 ≤ 28 - 28 +7b
-28 ≤ 7b
Divide both side by 7
-28/7 ≤ 7b/7
-4 ≤ b
Now combine both the expression as : b ≤ - 2 and -4 ≤ b
-4 ≤ b ≤ - 2