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Questions and Answers
How many terms are there in the expression $8a - 9ab + 17$?
How many terms are there in the expression $8a - 9ab + 17$?
What is the coefficient of the term $-9ab$ in the expression $8a - 9ab + 17$?
What is the coefficient of the term $-9ab$ in the expression $8a - 9ab + 17$?
What is the simplified form of the expression $5x - 3 + 8x + 2$?
What is the simplified form of the expression $5x - 3 + 8x + 2$?
What is the solution for $2x = 8$?
What is the solution for $2x = 8$?
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What is the simplified form of the expression $(7x - 5) - (4x - 12)$?
What is the simplified form of the expression $(7x - 5) - (4x - 12)$?
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What value of $x$ makes the equation $3 + rac{x}{4} = 14$ true?
What value of $x$ makes the equation $3 + rac{x}{4} = 14$ true?
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What is the solution for the equation $3 rac{x-6}{2} = 9$?
What is the solution for the equation $3 rac{x-6}{2} = 9$?
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How can the expression $2x + x + 7 + x + 3x + 4$ be simplified?
How can the expression $2x + x + 7 + x + 3x + 4$ be simplified?
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Study Notes
Learning Targets
- Perform operations with linear expressions and identify their components.
- Solve linear equations for a specific variable.
Expression Criteria
- Create an expression with three terms:
- The first term is a constant.
- The second term contains two variables.
- The third term has a positive coefficient.
Analyzing the Expression: 8𝑎 − 9𝑎𝑏 + 17
- Number of terms: Three
- List of terms: 8𝑎, −9𝑎𝑏, 17
- Constants: 17
- Coefficients: 8, -9 (for 𝑎 and 𝑏 respectively)
- Variables: 𝑎, 𝑏
Expression Simplification
- For 5𝑥 − 3 + 8𝑥 + 2:
- Simplified form: 13𝑥 - 1
- For (7𝑥 − 5) − (4𝑥 − 12):
- Simplified form: 3𝑥 + 7
- For 3(2𝑥 − 5):
- Simplified form: 6𝑥 - 15
- For 4𝑥 + 2(3 − 3𝑥):
- Simplified form: -2𝑥 + 6
Solving for x
- 2𝑥 = 8 → x = 4
- 6 + 𝑥 = 8 → x = 2
- 5𝑥 − 9 = 6 → x = 3
- 2𝑥 + 11 = −15 → x = −13/2
- 3(2𝑥 + 1) = 21 → x = 3
- 3𝑥 − 5 = 7𝑥 + 3 → x = -2
- −4𝑥 + 16 = −9𝑥 − 4 → x = 4
- 52 + 7𝑥 = 7𝑥 + 52 → Any value of x is a solution
- 6𝑥 − 7 = 7 + 6𝑥 → No solution
- 2𝑥 + 𝑥 + 7 + 𝑥 + 3𝑥 + 4 = 4𝑥 + 8 − 𝑥 − 3 → Simplifies to x = 3
Solution to 3𝑥 + 8 = 14
- Testing values:
- For c (2) → 3(2) + 8 = 14 (True)
- Other values (18, 66, 7) do not satisfy the equation.
Solving Additional Equations
- For 2/(x−6) = 9 → x = −6 + 2/9 (calculate step-wise)
- For 4/(2) = 7 → x = 1/2 (calculate step-wise)
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Description
Test your understanding of linear expressions and equations in this Algebra Class 10 Unit 1 review. You'll be tasked with writing expressions based on specified criteria and solving linear equations for a variable. Perfect for reinforcing your algebra skills!
