Solve linear inequalities using addition and subtraction. Grade 9 Alberta mathematics.
Lesson 6.4 of Linear Equations & Inequalities in Grade 9 Math — Alberta curriculum lessons.
Just like solving equations, we want to isolate the variable — but this time, we're working with inequality symbols instead of an equal sign.
When you add or subtract the same number on both sides of an inequality, the inequality stays true. That's called keeping the inequality balanced.
Balance Rule. Whatever you do to one side, you must do to the other side — just like an equation!
Sometimes, the variable (like x) appears on both sides of the inequality sign. Your goal is still the same — get x alone on one side using addition or subtraction.
To do that, you'll move one of the variable terms using inverse operations.
Balance Strategy. Whatever you do to one side, you must also do to the other — just like equations.
Solve: x - 5 > 7
Step 1: Identify What's Being Done. 5 is being subtracted from x
Step 2: Use the Inverse Operation. Add 5 to both sides
Step 3: Apply It. (x - 5) + 5 > 7 + 5
Step 4: Simplify. x > 12
✅ Answer: x > 12. x > 12
Check:. Pick x = 13: 13 - 5 = 8 → 8 > 7 ✓ True
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