Five less than three times the sum of a number and nine is at least 20.
sum of a number and nine ... x+9
three times that ... 3(x+9)
five less than that ... 3(x+9)-5
now finish it off
3(n+9) - 5 <= 20
3(n+9) - 5 >/=20
3 n + 27 - 5 >/= 20
3 n + 22 >/= 20
3 n >/= -2
n >/= -2/3
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check
if n = -2/3
n +9 =27/3 - 2/3 = 25/3
3(n+9) = 25
25-5 = 20 sure enough
at least ... >=
To solve this problem, we need to set up an equation and then solve for the unknown number.
Let's break down the problem statement:
"Five less than three times the sum of a number and nine" can be written as:
3 * (number + 9) - 5
"is at least 20" means that the expression is greater than or equal to 20, so we can write this as:
3 * (number + 9) - 5 ≥ 20
Now we can solve the inequality.
Step 1: Distribute the 3 to number + 9:
3 * number + 3 * 9 - 5 ≥ 20
Step 2: Simplify:
3 * number + 27 - 5 ≥ 20
3 * number + 22 ≥ 20
Step 3: Subtract 22 from both sides of the inequality:
3 * number ≥ 20 - 22
3 * number ≥ -2
Step 4: Divide both sides of the inequality by 3:
number ≥ -2 / 3
So, the solution to the inequality is number ≥ -2 / 3.
This means that any number greater than or equal to -2 / 3 satisfies the inequality.