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Harder equations and inequalities
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Now the unknown can appear on both sides, or inside brackets. The balance method still works.
Unknowns on both sides
Get the letters on one side first, by subtracting the smaller letter term.
5x + 3 = 2x + 18
Subtract 2x: 3x + 3 = 18. Subtract 3: 3x = 15. So x = 5.
5x + 3 = 2x + 18
Subtract 2x: 3x + 3 = 18. Subtract 3: 3x = 15. So x = 5.
Brackets and forming equations
Expand brackets first: 3(x − 2) = 21 → 3x − 6 = 21 → 3x = 27 → x = 9.
In a word problem, choose a letter for the unknown and write an equation. Angles x, 2x and 3x in a triangle: 6x = 180, so x = 30.
In a word problem, choose a letter for the unknown and write an equation. Angles x, 2x and 3x in a triangle: 6x = 180, so x = 30.
Inequalities
x < 4 means x is less than 4. x ≥ −2 means x is −2 or more.
Solve them like equations: 2x + 3 < 11 → 2x < 8 → x < 4.
Integers that satisfy −2 < n ≤ 3: −1, 0, 1, 2, 3.
Solve them like equations: 2x + 3 < 11 → 2x < 8 → x < 4.
Integers that satisfy −2 < n ≤ 3: −1, 0, 1, 2, 3.
Solve 4(x + 1) = 2x + 14.
- Expand: 4x + 4 = 2x + 14
- Subtract 2x: 2x + 4 = 14
- Subtract 4, then divide by 2: x = 5
Answer: x = 5
Collect the letter terms on one side, expand brackets first, and solve inequalities just like equations.
The interactive lesson includes the diagrams for this topic.
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