Ten times the sum of a number 15 and is at least 21

Question

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Answer 1

Let x = the number

"Ten times the sum of a number and 22 is at least 21" means
Ten times [the sum of a number and 22] is at least 21 means
10 * ( x + 22 ) ≥ 21

10(x+22) ≥ 21
10x + 220 ≥ 21 [distribute]
10x ≥ -199 [subtract 220 from both sides retains the sense of the inequality]
x ≥ -19.9 [divide both sides by 10 retains the sense of the inequality]

Check:
Use -20 [note: should be false]
Is 10(-20+22) ≥ 21 ?
10(2) ≥ 21 >
20 ≥ 21 ?no

Use 0 [note: should be true]
Is 10(0 + 22) ≥ 21 ?
220 ≥ 21 ?yes

Answer 2

Three times the sum of a number and 21 is less than 20