Question

How do you write the expression: Half of a number decreased by 7 is at least 5?

Answer 1

We use the meaning of each word given in the expression and write the expression step-by-step according to the sequence of words given in the expression.

• Half means one part when an item or a value is divided into parts. So, when we write half we numerically mean $\dfrac{1}{2}$.
• Decreased means lowering the value or subtracting the value.
• At least means there can be more than that value but it is necessary to have that value.

Complete step-by-step answer:
We have to form an expression for the statement: Half of a number decreased by 7 is at least 5
We use the definitions of half, decreased and at least to form the expression.
Let us assume a number ‘x’ … (1)
Then half of the number will be $\dfrac{x}{2}$ … (2)
Now decrease the half of number obtained in equation (2) by 7
i.e. Subtract 7 from half of the number in equation (2) , i.e. $\left( {\dfrac{x}{2} - 7} \right)$ … (3)
Now we are given that this value is at least 5, so we can write the value in equation (3) will be greater than or equal to 5.
$\Rightarrow \left( {\dfrac{x}{2} - 7} \right) \geqslant 5$ … (4)

$\therefore$The expression: Half of a number decreased by 7 is at least 5 can be written as $\left( {\dfrac{x}{2} - 7} \right) \geqslant 5$

Note:
Many students make the mistake of writing at least part of the expression with $\leqslant$ or $<$ as they think least means less and these both signs are for less than or equal to and less than respectively. Keep in mind at least means it has the least value as given and can have higher values as well.