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Convert given statement to equation form: Five times a number increased by \[7\] is \[27\] .

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Last updated date: 17th Jul 2024
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Answer
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Hint: First we have to define what the terms we need to solve the problem are.
An equation is a mathematical sentence that has two equal sides separated by an equal sign. \[{\text{3 + }}6 = 9\] is an example of an equation. We can see on the left side of the equal sign, \[3 + {\text{ }}6\] , and on the right-hand side of the equal sign, $ 9 $ .

Complete step by step answer:
Let $ x $ be the unknown number
When you 'multiply' or 'times' a number you add it to itself a number of times, for example $ 4 $ multiplied by $ 3 $ is the same as saying \[4{\text{ }} + {\text{ }}4{\text{ }} + {\text{ }}4{\text{ }} = {\text{ }}12\] .Multiplication is therefore a quicker way of adding the same number many times, for example \[3{\text{ }} \times {\text{ }}4{\text{ }} = {\text{ }}12.\]
Thus, from given question it is denoted as five times the number $ 5x $ [since $ x $ is the unknown value from the given problem]
Increase by means to take an amount and add another specified amount to it. For example, take one apple, and increase by five. So, you have \[1\] , and then you add $ 5 $ apples. Now you end up with six apples
Hence from the given question five times a number increased by \[7\] means \[5x + 7\] (adding \[7\] with respect to the fives times the unknown $ x $ )
[Finally, the equal sign in mathematics describes equality between the values, equations, or expressions written on both sides. The symbol for equal to be two small horizontal lines placed paralleled. We place the 'equal to' sign between two things that are the same or equal. Examples: $ 1 + 1 = 2 $ .]
Hence the required equation is $ 5x + 7 = 27 $

Note: An equation is a mathematical sentence that has two equal sides separated by an equal sign. Since increased denotes adding, decreased will denote subtraction. Also, times will denote multiplication for an equating problem like this.