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How do you simplify \[2\left( 3x-1 \right)+3x+4\]?

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Last updated date: 20th Jun 2024
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Answer
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Hint: This is a linear equation in one variable as there is only one variable in an equation. In the given question, the variable is the letter ‘\[x\]’. To solve this equation, we need to perform mathematical operations such as addition, subtraction, multiplication and division. To solve the given question, we here need to use the distributive property of arithmetic operation.

Formula used:Distributive property of multiplication over subtraction states that the product of a number say ‘a’ with product of two numbers, say ‘b’ and ‘c’ is equal to the subtraction of products of the number ‘a’ multiplied separately with ‘b’ and ‘c’:
\[a\times \left( b-c \right)=ab-ac\]

Complete step-by-step solution:
We have the given linear equation:
\[2\left( 3x-1 \right)+3x+4\]
Distribute 2 to the \[3x-1\]by using distributive property, we get
\[6x-2+3x+4\]
By combining the like terms containing\[x\], we get
\[9x-2+4\]
Adding the numbers, we get
\[9x+2\]

Therefore, \[9x+2\] is the required simplification of the given equation \[2\left( 3x-1 \right)+3x+4\].

Note: We note that the polynomial with degree 1 is called the linear polynomial. To solve these types of questions, we need to know there are 4 properties for the arithmetic operation called closure, commutative, associative and distributive. The distributive property of multiplication requires one more operation either addition or subtraction. We know that the Distributive property of multiplication over subtraction states that the product of a number say ‘a’ with product of two numbers, say ‘b’ and ‘c’ is equal to the subtraction of products of the number ‘a’ multiplied separately with ‘b’ and ‘c’:
\[a\times \left( b-c \right)=ab-ac\]