10 Questions
Linear equations play a fundamental role in ______, particularly in solving problems involving measurements such as area of geometric shapes like squares and rectangles.
algebra
To solve the linear equation ax + b = c, where x is the unknown value, and a, b, and c are known values, you need to ______ the variable.
isolate
These equations consist of two variables connected by an equal sign with one variable standing alone on either side of the ______.
equation
In the equation 3x - 7 = 8, we want to ______ the x to find its value.
isolate
After isolating the variable in a linear equation, you need to apply inverse operations to find the actual ______ of the variable.
value
मराठी साहित्यातील प्राचीन खालच्या काळात, ज्ञानेश्वर, तुकाराम, नामदेव यांच्या ______ आणि अभंगांमध्ये महत्त्वपूर्ण योगदान आहे.
अभंग
१८५१ नंतर कविता लेखनाचे महत्त्व वाढत होते, पहिले इंग्रजी कादंबर्यांचे भाषांतर केले जाते, नंतर लघु साहित्यिक मराठीतील मूळ संगणकांवर लिहितले जाते, ह्या काळात बाल गंगाधर तिलक, महादेव शास्त्री जोशी, नारायण हृदय कर्वे, जी.एस. घुर्ये, बहिणाबाई चौधरी, बाबुराव बागुळ, विक्रम सराभाई, वाय.बी. चव्हाण, डॉ. अंबेडकर, नीलकंठ ठाकरे, शरत्चंद्र छत्रपत्ती, राजा धुराळीकर, प्रल्हाद केशव अत्रे, आणि महादेवी वर्मा यांच्या ______ आहेत.
लेखन
समकालीन मराठी साहित्यात विविध प्रकारांमध्ये वागण्यारी, अलेखात्मक, नाटक, लघुकथा, बालसाहित्य, प्रवासवृत्तांत, जीवनचरित्रे, आणि स्वतंत्र लेखनांसह समाविष्ट आहे.
अंगीकार
आजच्या काळात, मराठी साहित्यात गिरीश कर्नाड, उदय प्रकाश, अरुण कोलटकर आणि विजय दान देथा यांच्या ______ आहेत.
कल्पना
मराठी साहित्याच्या उत्तर वर्गातील विविध काव्यरचनांचा संग्रह पहिल्यांदा संस्कृतातून व्यक्त झाला, आणि आता सामाजिक बदलांच्या, सांस्कृतिक पहचाणाच्या, आणि व्यक्तिमत्वाच्या ______ंकडे विस्तृत आहे.
परिप्रेक्ष्या
Study Notes
Linear Equations
Linear equations play a fundamental role in algebra, particularly in solving problems involving measurements such as area of geometric shapes like squares and rectangles. These equations consist of two variables connected by an equal sign with one variable standing alone on either side of the equation. Here's how you can solve them using one of their most basic forms: ax + b = c, where x is the unknown value, and a, b, and c are known values.
To solve this type of equation, follow these steps:
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Isolate the variable: In the given equation, try to isolate the variable (x) to one side of the equation. For example, if x represents some quantity, say distance, it might appear in more than one place in the equation; your goal is to move all these instances together so they only appear once. This may involve adding or subtracting numbers from both sides of the equation until one term containing the variable is isolated.
Example: If we have the equation (3x - 7 = 8), we would want to isolate the (x): [ 3x - 7 \equiv {\color{blue} 3} \ 3x - 7 + 7 \equiv{\color{green}{7}} \ 3x \equiv_{10} \ x \equiv_3 ]
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Calculate the result: After successful isolation, apply inverse operations to find the actual value of the variable. Continuing our previous example: [ 3x \equiv_3 \ \frac{3x}{\color{yellow} 3} \equiv_{\frac{1}{3}}\text{(since } \frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}\text{)} \ x \equiv_1 ]
In conclusion, understanding and working with linear equations requires mastery of basic arithmetic operations along with the ability to manipulate expressions without changing their formal mathematical attributes. As you practice more complex scenarios, keep in mind that every step must leave the original equality true and the final answer correct regardless of which variable name appears on either side of the equal sign.
Learn how to solve linear equations in the basic form of 'ax + b = c', where x is the unknown value, and a, b, and c are known values. Understand the steps involved in isolating the variable and calculating its value using inverse operations. Practice mastering basic arithmetic while manipulating expressions to maintain the equality of the equation throughout the solving process.
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