Fill in the gap to factorise this expression
[tex]$10 x+15=-(2 x+3)$[/tex]
Answer (2)
Expand the right side of the equation: 10 x + 15 = − 2 x − 3 .
Move all terms to the left side: 10 x + 15 + 2 x + 3 = 0 .
Combine like terms: 12 x + 18 = 0 .
Factor out the greatest common divisor: 6 ( 2 x + 3 ) = 0 . The factorised expression is 6 ( 2 x + 3 ) = 0 .
Explanation
Understanding the Problem We are given the equation 10 x + 15 = − ( 2 x + 3 ) and asked to 'factorise' it. It seems like the intention is to rearrange the equation and then factorise the resulting expression.
Expanding the Equation First, we expand the right side of the equation:
10 x + 15 = − 2 x − 3
Rearranging the Equation Next, we move all terms to the left side of the equation by adding 2 x and 3 to both sides:
10 x + 15 + 2 x + 3 = 0
Combining Like Terms Now, we combine like terms:
12 x + 18 = 0
Factoring out the GCD We can factor out the greatest common divisor (GCD) from the left side. The GCD of 12 and 18 is 6. So we factor out 6:
6 ( 2 x + 3 ) = 0
Final Factorised Form Therefore, the factorised expression is 6 ( 2 x + 3 ) = 0 . We can also divide both sides by 6 to get 2 x + 3 = 0 .
Examples
Factoring expressions is a fundamental skill in algebra and is used extensively in various real-world applications. For instance, in engineering, factoring can help simplify complex equations that model physical systems, making them easier to analyze and solve. In economics, factoring can be used to analyze cost functions and optimize production processes. Moreover, in computer science, factoring is used in cryptography to secure data transmission and storage. Understanding how to factor expressions allows us to break down complex problems into simpler, more manageable parts, leading to more efficient and effective solutions.
To factorise the equation 10 x + 15 = − ( 2 x + 3 ) , we rearrange and combine like terms to get 12 x + 18 = 0 , then factor out the GCD to reach 6 ( 2 x + 3 ) = 0 . The factorised form reveals potential solutions for x .
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