the sum of a number times 8 and 15 is at most -22
To solve the inequality, let's create an equation using the given information.
Let's assume the number is represented by 'x'.
The sum of a number times 8 and 15 is at most -22 can be written as:
8x + 15 ≤ -22
Now, we can solve the equation for 'x' step-by-step.
1. Subtract 15 from both sides of the inequality:
8x + 15 - 15 ≤ -22 - 15
8x ≤ -37
2. Divide both sides by 8 to solve for 'x':
(8x) / 8 ≤ (-37) / 8
x ≤ -37/8
Therefore, the solution to the inequality is:
x ≤ -37/8
To find the solution to this problem, let's break it down step by step.
We have the phrase "the sum of a number times 8 and 15" which can be translated into an equation. Let's represent the unknown number with the variable "x".
The equation can be written as:
8x + 15
We are given that this sum is at most -22. This means that the expression on the left side of the equation should be less than or equal to -22. So, we can write the inequality as:
8x + 15 ≤ -22
To find the solution for x, we need to isolate the variable. Let's start by subtracting 15 from both sides of the equation:
8x + 15 - 15 ≤ -22 - 15
Simplifying this, we get:
8x ≤ -37
Now, we can divide both sides of the inequality by 8 to solve for x:
(8x) / 8 ≤ (-37) / 8
Simplifying further:
x ≤ -37/8
So, the solution to the inequality is x ≤ -37/8.
Therefore, the sum of a number times 8 and 15 is at most -22 when the number is less than or equal to -37/8.
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