2.2 Linear Equations

• Meaning of a linear equation in one unknown
• Forming linear equations in one unknown from situations
• Solving linear equations using inverse operations (add and subtract)
• Solving linear equations using inverse operations (multiply and divide)
• Beam balance and shopping as models of equations
• Checking a solution by substitution
• Applying and reflecting on linear equations in real life

• form linear equations in one unknown in different situations
• solve linear equations in one unknown in different situations
• apply linear equations in one unknown to real-life situations
• reflect on the use of linear equations in real-life situations

“How do we use linear equations in real-life?”

“Why do we use linear equations in real-life?”

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1. What a linear equation is
   40 min · 1 practice tasks · quiz
   A linear equation in one unknown is a balanced sentence with one letter to the first power, modelled by a level beam.
2. Form linear equations in one unknown
   40 min · 1 practice tasks · quiz
   Turn shopping, age and beam stories into equations such as x + 5 = 12 and 3p = 90.
3. Solve by adding or subtracting
   40 min · 1 practice tasks · quiz
   Isolate the unknown by doing the inverse add or subtract on both sides, then check by substitution.
4. Solve by multiplying or dividing
   40 min · 1 practice tasks · quiz
   Undo a coefficient by dividing both sides, undo a denominator by multiplying, then solve two-step equations.
5. Apply equations to shopping and weighing
   40 min · 1 practice tasks · quiz
   Form and solve equations from a kiosk bill and a beam balance, then check that both sides still match.
6. Reflect on equations in real life
   40 min · 1 practice tasks · quiz
   Say how and why linear equations are used: to find one unknown fairly, to plan a bill, and to check a guess.