Five times the sum of a number and 28 is at most -15
Let the number be p
And 28
Then 5 times the sum is at most
5(P+28)≤-15
Let's break down the problem step by step.
Step 1: Express "a number" as a variable
Let's represent "a number" as the variable x.
Step 2: Translate the given information into an equation
The phrase "Five times the sum of a number and 28" can be translated as 5(x + 28). The word "is" can be translated as an equal sign (=). The phrase "at most -15" can be translated as "less than or equal to -15" (≤ -15).
So, our equation becomes:
5(x + 28) ≤ -15
Step 3: Solve the equation
Distribute 5 to the terms inside the parentheses:
5x + 5(28) ≤ -15
Simplify:
5x + 140 ≤ -15
Subtract 140 from both sides to isolate the variable term:
5x + 140 - 140 ≤ -15 - 140
5x ≤ -155
Step 4: Final solution
Divide both sides of the inequality by 5 to solve for x:
(5x)/5 ≤ (-155)/5
x ≤ -31
So, the solution is x ≤ -31.
To solve this problem, we need to set up an inequality equation and then solve for the number.
Let's assume the number is represented by "x". The sum of a number and 28 is written as (x + 28).
We are given that five times the sum of a number and 28 is at most -15. We can write this as:
5(x + 28) ≤ -15
Now, we can solve the inequality equation to find the range of values for "x" that satisfy the given condition.
To solve the inequality, we will begin by distributing the 5 to both terms inside the parentheses:
5x + 140 ≤ -15
Next, we can isolate the variable term by subtracting 140 from both sides of the inequality:
5x ≤ -15 - 140
5x ≤ -155
Finally, to solve for "x", we divide both sides by 5:
x ≤ -155/5
x ≤ -31
Therefore, the range of values for "x" that satisfy the given inequality is x ≤ -31.