Six times the sum of a number and 18 is at most 19
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6 (n + 18) ≤ 19
Let's solve the inequality step-by-step:
1. "A number" can be represented by the variable 'x'.
2. The sum of a number and 18 is x + 18.
3. "Six times the sum of a number and 18" is 6(x + 18).
4. The inequality can be written as: 6(x + 18) ≤ 19.
5. Distribute the 6 to both terms inside the parentheses: 6x + 108 ≤ 19.
6. Subtract 108 from both sides of the inequality: 6x ≤ 19 - 108.
7. Simplify the right side of the inequality: 6x ≤ -89.
8. Divide both sides of the inequality by 6: x ≤ -89/6.
Therefore, the value of 'x' must be less than or equal to -89/6 for the inequality 6(x + 18) ≤ 19 to hold true.
To solve this equation, let's first define a variable. Let's say the number we're trying to find is represented by the variable "x."
The equation "six times the sum of a number and 18 is at most 19" can be written as:
6(x + 18) ≤ 19
To solve this equation, we will isolate the variable x and find its value.
Step 1: Distribute the 6 to the terms inside the parentheses:
6x + 108 ≤ 19
Step 2: Move 108 to the other side of the inequality by subtracting it from both sides:
6x + 108 - 108 ≤ 19 - 108
6x ≤ -89
Step 3: Divide both sides of the inequality by 6 to isolate x:
(6x)/6 ≤ (-89)/6
x ≤ -89/6
Therefore, the value of x is less than or equal to -89/6.
As for interpreting the result, it means that any number equal to or less than -89/6, when plugged into the original equation, will satisfy the inequality.