Question

How do you write an inequality and solve given “three times the sum of a number and seven is greater than five times the number less thirteen”?

Answer 1

Hint: From the given question, we have been asked to write an inequality and also to solve it. And give that, “three times the sum of a number and seven is greater than five times the number less than thirteen”. Now, what we have to do is, separate the statements and have to write the inequality.

Complete step-by-step answer:
First of all, let us assume the number as \[n\].
Now, the sum of this number and \[7\] can be written as \[n+7\]
Now, given that three times the sum, it can be represented as \[3\left( n+7 \right)\].
Now, we have to write the expression for, five times number less thirteen.
It can be represented as \[5n-13\].
Now, the inequality can be written as \[3\left( n+7 \right) > 5n-13\]
The above represented expression is the inequality which we have been asked to find.
Also, we have been asked to solve the inequality.
Inequality we got is \[3\left( n+7 \right) > 5n-13\]
First, distribute the brackets on the left side, by distributing the brackets, we get \[3n+21 > 5n-13\]
Subtract \[3n\] from both sides of the inequality. By subtracting, we get \[3n-3n+21 > 5n-3n-13\]
\[\Rightarrow 21 > 2n-13\]
Now, add \[13\] to the both sides of the inequality. By adding \[13\] to the both sides of the inequality, we get
\[21+13 > 2n-13+13\]
\[\Rightarrow 34 > 2n\]
Now, divide the both sides of the inequality by \[2\]. By dividing the both sides of the inequality by \[2\], we get \[17 > n\Rightarrow n < 17\]
Hence, the obtained inequality is solved.

Note: We should understand the question correctly by reading it twice or thrice. After understanding we have to write the inequality by the given statements. Then we should be careful while solving the obtained inequality. Also, we should be careful while writing the inequality. Also, we should be careful while converting the given statement into mathematical expression. Similarly we can solve the inequality given by the statement “four times the sum of a number and eight is greater than five times the number less thirteen” mathematically given as \[4\left( n+8 \right) > 5n-13\Rightarrow 4n+32 > 5n-13\Rightarrow 32+13 > n\Rightarrow n < 45\] .