What is 6 less than a number t is 7?
The correct answer and explanation is:
To express the phrase “6 less than a number t is 7” algebraically, you start by translating the words directly into mathematical symbols.
The phrase “a number t” represents the variable t, which can be any number. The phrase “6 less than” means that 6 is subtracted from this number t. So, “6 less than t” can be written as:
t – 6
The phrase “is 7” indicates an equation where the expression t – 6 is equal to 7. Therefore, the equation becomes:
t – 6 = 7
Now, to solve for t, you need to isolate the variable t on one side of the equation. To do this, you add 6 to both sides of the equation. This is based on the principle of equality, which states that if you add or subtract the same value from both sides of an equation, the equality remains true.
So, adding 6 to both sides:
t – 6 + 6 = 7 + 6
This simplifies to:
t = 13
Therefore, the solution to the equation t – 6 = 7 is t = 13.
To check the solution, you can substitute t = 13 back into the original equation:
13 – 6 = 7
This is a true statement, confirming that t = 13 is the correct solution. The number t that satisfies the condition “6 less than it equals 7” is 13.
This is a simple example of how algebra can be used to translate verbal phrases into mathematical expressions and solve for unknown values.