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2x-1/3-6x-2/5=1/3
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2x-1/3-6x-2/5=1/3
To solve the equation 2x - 1/3 - 6x - 2/5 = 1/3, we need to simplify the expression on the left side and isolate the variable x. Let's break down the steps to solve this equation.
1. Combine like terms:
- The given equation has two terms with x, which are 2x and -6x. Combine these terms by subtracting 6x from 2x, which gives us -4x.
- The equation now becomes -4x - 1/3 - 2/5 = 1/3.
2. Find the common denominator:
- To add or subtract fractions, we need to have a common denominator. In this case, the denominators of the fractions are 3 and 5. The least common denominator (LCD) for 3 and 5 is 15.
- Multiply the numerator and denominator of the first fraction (-1/3) by 5, and multiply the numerator and denominator of the second fraction (-2/5) by 3. This gives us -5/15 and -6/15, respectively.
- The equation is now -4x - 5/15 - 6/15 = 1/3.
3. Combine the fractions:
- Since both fractions now have the same denominator of 15, we can add them together. -5/15 and -6/15 combine to give us -11/15.
- The equation becomes -4x - 11/15 = 1/3.
4. Isolate the variable:
- To isolate the variable x, we need to move the constant term (-11/15) to the other side of the equation.
- Since -11/15 is subtracted from -4x, we can add it to both sides of the equation to eliminate it from the left side.
- The equation becomes -4x = 1/3 + 11/15.
5. Add the fractions on the right side:
- To add the fractions 1/3 and 11/15, we need to find a common denominator. The LCD for 3 and 15 is 15. Multiply the numerator and denominator of 1/3 by 5 to get 5/15.
- The equation simplifies to -4x = 5/15 + 11/15, which is -4x = 16/15.
6. Solve for x:
- To solve for x, divide both sides of the equation by -4. This eliminates the coefficient -4 in front of x.
- The equation becomes x = (16/15) / -4.
7. Simplify the expression:
- To divide a fraction by a whole number, we can multiply the fraction by the reciprocal of the whole number. The reciprocal of -4 is -1/4.
- Multiply (16/15) by (-1/4) to get -16/60, which simplifies to -4/15.
- Therefore, the solution to the equation is x = -4/15.
In summary, the solution to the equation 2x - 1/3 - 6x - 2/5 = 1/3 is x = -4/15.
1. Combine like terms:
- The given equation has two terms with x, which are 2x and -6x. Combine these terms by subtracting 6x from 2x, which gives us -4x.
- The equation now becomes -4x - 1/3 - 2/5 = 1/3.
2. Find the common denominator:
- To add or subtract fractions, we need to have a common denominator. In this case, the denominators of the fractions are 3 and 5. The least common denominator (LCD) for 3 and 5 is 15.
- Multiply the numerator and denominator of the first fraction (-1/3) by 5, and multiply the numerator and denominator of the second fraction (-2/5) by 3. This gives us -5/15 and -6/15, respectively.
- The equation is now -4x - 5/15 - 6/15 = 1/3.
3. Combine the fractions:
- Since both fractions now have the same denominator of 15, we can add them together. -5/15 and -6/15 combine to give us -11/15.
- The equation becomes -4x - 11/15 = 1/3.
4. Isolate the variable:
- To isolate the variable x, we need to move the constant term (-11/15) to the other side of the equation.
- Since -11/15 is subtracted from -4x, we can add it to both sides of the equation to eliminate it from the left side.
- The equation becomes -4x = 1/3 + 11/15.
5. Add the fractions on the right side:
- To add the fractions 1/3 and 11/15, we need to find a common denominator. The LCD for 3 and 15 is 15. Multiply the numerator and denominator of 1/3 by 5 to get 5/15.
- The equation simplifies to -4x = 5/15 + 11/15, which is -4x = 16/15.
6. Solve for x:
- To solve for x, divide both sides of the equation by -4. This eliminates the coefficient -4 in front of x.
- The equation becomes x = (16/15) / -4.
7. Simplify the expression:
- To divide a fraction by a whole number, we can multiply the fraction by the reciprocal of the whole number. The reciprocal of -4 is -1/4.
- Multiply (16/15) by (-1/4) to get -16/60, which simplifies to -4/15.
- Therefore, the solution to the equation is x = -4/15.
In summary, the solution to the equation 2x - 1/3 - 6x - 2/5 = 1/3 is x = -4/15.
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2x-1/3-6x-2/5=1/3 for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about 2x-1/3-6x-2/5=1/3 covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2x-1/3-6x-2/5=1/3.
2x-1/3-6x-2/5=1/3 for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about 2x-1/3-6x-2/5=1/3 covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2x-1/3-6x-2/5=1/3.
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