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MTH1W Grade 9 Mathematics 4.1 Solving Simple Equations Goal(s) To develop strategies to use to find the root or solution to onestep and two step equations Isolate the variable using opposite operations and maintaining balance within the equation An equation is a mathematical statement that says two expressions are equal:
3x + 3 = 2x ‑ 1
To solve an equation means to find the value of the variable that makes the statement true. This is also called finding the root of the equation. Equations can be solved: using algebra tiles by inspection by isolating the variable using opposite operations while maintaining balance within the equation.
Solving by Inspection Sometimes it is possible to solve an equation by inspection , which means just looking at it and applying number sense. When an equation can't be solved by inspection, use opposite operations to isolate the variable and find the solution. Operation Opposite
Solving Twostep Equations To solve equations taking two steps, use opposite operations and apply BEDMAS in reverse (SAMDEB!). To isolate x , it is necessary to undo the operations in the equation. Start by subtracting 7 from both sides. Second divide both sides by 2. 2x + 7 = 9 2x + 7 ‑ 7 = 9 ‑ 7 2x = 2 2x = 2 x = 1 (^2 ) Solve each equation by isolating the variable using opposite operations and maintaining balance within the equation. a) (^) 4x + 7 = 27 b) w ‑ 4 = 11 3
To check if your solution is correct, substitute the root into the left side and right side of the equation. Both sides must be equal. Solve each equation by isolating the variable using opposite operations and maintaining balance within the equation. Check your answer. Check L.S. R.S.
2x + 4 = 8
= 2x + 4 = 8
