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Word Linear Inequalities
Translate English into an inequality, then solve. 'Four more than three times x is less than 40' is 3x+4<40. Area and weight limits become <= or >. The algebra is Chapter 4; the sentence is the extra step. Units stay in the sentence, not mixed into x blindly.
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Word Linear Inequalities
What is it?
Translate English into an inequality, then solve. 'Four more than three times x is less than 40' is 3x+4<40. Area and weight limits become <= or >. The algebra is Chapter 4; the sentence is the extra step. Units stay in the sentence, not mixed into x blindly.
In simple words
- Translate English into an inequality, then solve.
- PHRASES: 'Less than' is <.
- AREA / WEIGHT: Rectangle height 9, width x+2, area>81: 9(x+2)>81.
- Worked-method reminder: x > 7
Important terms
WORD LINEAR INEQUALITIES: Translate English into an inequality, then solve. 'Four more than three times x is less than 40' is 3x+4<40. Area and weight limits become <= or >. The algebra is Chapter 4; the sentence is the extra step. Units stay in the sentence, not mixed into x blindly.
PHRASES: 'Less than' is <. 'At most / no more than' is <=. 'At least' is >=. Twice the sum of x and 8 is 2(x+8), not 2x+8 unless the 'twice' hits only x.
AREA / WEIGHT: Rectangle height 9, width x+2, area>81: 9(x+2)>81. Triangle area 12 8 (x+1) <= 44. Bag 26.5 plus w at most 60: 26.5+w<=60.
What you should learn
- Explain word linear inequalities using the correct definitions, conditions, and notation.
- Apply translate, then solve correctly in routine and exam-style questions.
- Show each important step, simplify the result, and check that it satisfies the original conditions.
Examples
- 3x+4<40
- 2(x+8)<=-2
- x+2 is a width, not an area
PHRASES
'Less than' is <. 'At most / no more than' is <=. 'At least' is >=. Twice the sum of x and 8 is 2(x+8), not 2x+8 unless the 'twice' hits only x.
AREA / WEIGHT
Rectangle height 9, width x+2, area>81: 9(x+2)>81. Triangle area 12 8 (x+1) <= 44. Bag 26.5 plus w at most 60: 26.5+w<=60.
Recommended for Class 10
Full school-level explanation
Translate English into an inequality, then solve. 'Four more than three times x is less than 40' is 3x+4<40. Area and weight limits become <= or >. The algebra is Chapter 4; the sentence is the extra step. Units stay in the sentence, not mixed into x blindly.
Words to symbols:
WHAT — WORD LINEAR INEQUALITIES
Translate English into an inequality, then solve. 'Four more than three times x is less than 40' is 3x+4<40. Area and weight limits become <= or >. The algebra is Chapter 4; the sentence is the extra step. Units stay in the sentence, not mixed into x blindly. The symbols and conditions are part of the mathematics, so include them when stating the rule.
WHY — Why this topic matters
Word Linear Inequalities matters because inequalities describe ranges and limits rather than one exact value. They are used for constraints, graphs, optimisation, and real situations such as budgets, dimensions, and capacity.
HOW — How to solve and explain it
Start by identifying what is given and what must be found. Work through PHRASES, then AREA / WEIGHT. Worked: 9 ft by (x+2) ft rectangle, area > 81. 9(x + 2) > 81 x + 2 > 9 x > 7 Finish by checking signs, restrictions, units, and whether the answer matches the question.
PHRASES
'Less than' is <. 'At most / no more than' is <=. 'At least' is >=. Twice the sum of x and 8 is 2(x+8), not 2x+8 unless the 'twice' hits only x.
Remember
- at most = <=
Examples
- 3x+4<40
- 2(x+8)<=-2
- x+2 is a width, not an area
AREA / WEIGHT
Rectangle height 9, width x+2, area>81: 9(x+2)>81. Triangle area 12 8 (x+1) <= 44. Bag 26.5 plus w at most 60: 26.5+w<=60.
Remember
- write the formula first
Examples
- 9(x+2)>81 -> x>7
- 4(x+1)<=44 -> x<=10
- w<=33.5
Remember
- translate, then solve
- x > 7
- half base times height
- at most = <=
- write the formula first
- translate, then solve
- translate, then solve
- mathematical reasoning
How the ideas connect
Worked: 9 ft by (x+2) ft rectangle, area > 81. 9(x + 2) > 81 x + 2 > 9 x > 7
Deeper understanding
Go beyond memorising Word Linear Inequalities. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked: 9 ft by (x+2) ft rectangle, area > 81. 9(x + 2) > 81 x + 2 > 9 x > 7
Common mistakes
Exam focus
Core Idea
PHRASES
AREA / WEIGHT
Worked Method
Exam focus
Quick revision
- translate, then solve
- x > 7
- half base times height
- at most = <=
- WORD LINEAR INEQUALITIES: Translate English into an inequality, then solve. 'Four more than three times x is less than 40' is
- PHRASES: 'Less than' is <. 'At most / no more than' is <=. 'At least' is >=. Twice the sum of x and 8 is 2(x+
Area of a triangle is (12) base height. Forgetting 12 doubles the bound on x.
For long answers on Word Linear Inequalities: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- translate, then solve
- x > 7
- half base times height
- at most = <=
Important formulas
- translate, then solve
- x > 7
- half base times height
Common exam traps
- Area of a triangle is (12) base height. Forgetting 12 doubles the bound on x.
- Do not treat PHRASES and AREA / WEIGHT as the same step; each has a different purpose.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Area of a triangle is (12) base height. Forgetting 12 doubles the bound on x.
- Mistake
Do not treat PHRASES and AREA / WEIGHT as the same step; each has a different purpose.
- Mistake
Do not jump straight to the answer; omitted signs, brackets, restrictions, or construction reasons can change the result.
- Mistake
Area of a triangle is (12) base height. Forgetting 12 doubles the bound on x.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
translate, then solve
x > 7
half base times height
at most = <=
Translate English into an inequality, then solve. 'Four more than three times x is less than 40' is 3x+4<40. Area and weight limits become <= or >. The algebra
at most = <=
- Definition
- Translate English into an inequality, then solve. 'Four more than three times x is less than 40' is 3x+4<40. Area and weight limits become <= or >. The algebra
- Formula
- at most = <=
- Example
- 3x+4<40
- Critical warning
- Area of a triangle is (12) base height. Forgetting 12 doubles the bound on x.
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Exam Practice
Define
Q1. Define Word Linear Inequalities.
Explain
Q2. Explain: PHRASES.
Example
Q3. Give one clear example of Word Linear Inequalities and say why it fits.
Mistake
Q4. State one common mistake students make about Word Linear Inequalities.
Exam note
Q5. Write a short exam note on Word Linear Inequalities: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.