Question

How do you write an equation from the phrase “Seven less than twice a number is equal to \[19\]”?

Answer 1

Hint: According to the question, first we have to give a name to the value, or we can say that we have to assign a variable to the number. After that, we have to equate an equation according to the question. We have to go word by word in this question to get our equation.

Complete step by step solution:
First, we have to assign a variable to the number. So, let the number be \[x\]. Then, we will look at the phrase part where it is saying “twice a number”. The meaning of this here is that we have to multiply \[2\] to the number \[x\]. Now, we can see that the number is equal to \[19\]. The meaning of this here is that twice the number is equal to \[19\]. If we make an equation of this, then we get:
\[2x = 19\]

Now, the last thing which we have to look at is the phrase “Seven less”. The meaning of this here is that seven is subtracted from the number. The question here is “Seven less than twice a number is equal to \[19\]”. From here we can get that seven is subtracted from twice the number. If we equate this, then we get:
\[2x - 7 = 19\]

Now, if we want to solve the question, then we have to add \[7\] on both the sides. After that we get:
\[2x - 7 + 7 = 19 + 7\]
Here, after simple addition and subtraction we get that:
\[ \Rightarrow 2x = 26\]
Now, we have to just divide \[2\] on both the sides, and then we get:
\[ \Rightarrow \dfrac{{2x}}{2} = \dfrac{{26}}{2}\]
\[ \therefore x = 13\]

From here, we get our final answer as \[x = 13\].

Note: The above solving method is very easy but, we can solve the equation by another method. We can shift \[ - 7\] to the right side so that it gets grouped with its like terms. When \[ - 7\] is shifted to the other side, its sign changes and it gets added with \[19\] and the result is \[26\]. After that the \[2\] which is multiplied with \[x\]when shifted to the right side gets divided by \[26\] and the answer is \[13\].