Algebra Class 10 Unit 1 Review

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)