To translate the given sentence into an equation, we need to understand the mathematical operations described by the language used.
The sentence states: "If 7 is subtracted from the product of 3 and x, the result is 20."
Breaking this down:
1. "The product of 3 and x" means we multiply 3 by a variable x, which gives us the expression 3x.
2. "If 7 is subtracted from" means we subtract 7 from the expression we obtained previously, which would be represented as 3x - 7.
3. "The result is 20" expresses that after the subtraction, the outcome equals 20, which gives us the equality 3x - 7 = 20.
Now, let's solve the equation step by step:
The original equation we've translated is:
[tex]\[3x - 7 = 20\][/tex]
To solve for x, follow these steps:
Step 1: Add 7 to both sides of the equation to isolate the term with x on one side.
[tex]\[3x - 7 + 7 = 20 + 7\][/tex]
This simplifies to:
[tex]\[3x = 27\][/tex]
Step 2: Now divide both sides of the equation by 3 to solve for x.
[tex]\[\frac{3x}{3} = \frac{27}{3}\][/tex]
Simplifying the above equation gives us:
[tex]\[x = 9\][/tex]
So the solution to the equation is x = 9.
