Three times a number r plus 8 is fewer than -12
3 r + 8 < -12
3 r < -20
r <-20/8
r < - 2 1/2
r < -20/3
To solve this equation, we can start by translating the given statement into a mathematical equation.
The phrase "Three times a number r plus 8" can be represented as 3r + 8.
The word "fewer" indicates that we should subtract something. In this case, it is telling us to subtract -12.
So, we can set up the equation:
3r + 8 < -12
To isolate the variable r, we need to get rid of the 8. We can do this by subtracting 8 from both sides of the equation:
3r + 8 - 8 < -12 - 8
3r < -20
Finally, to solve for r, divide both sides of the inequality by 3:
(3r)/3 < -20/3
r < -20/3
So the solution for r is r < -20/3.
To solve this problem, we need to translate the given sentence into an equation and then solve for the variable "r".
Let's break down the information given:
"Three times a number r" can be written as 3r.
"Plus 8" means to add 8 to 3r.
"Is fewer than" represents the inequality symbol "<".
"-12" is the value we are comparing to.
Combining these, we can write the equation:
3r + 8 < -12
Now, to solve for "r", we will isolate the variable by performing the necessary algebraic operations:
1. Subtract 8 from both sides of the inequality:
3r + 8 - 8 < -12 - 8
3r < -20
2. Divide both sides of the inequality by 3 to isolate "r":
(1/3) * 3r < (-20) / 3
r < -20/3
Therefore, the solution to the equation is r < -20/3.