Mathematics Specification A - 4MA1 PearsonEdexcel

Inequalities

Gbogbo ọrọ náà

Inequalities describe relationships where one quantity is greater than, less than, or not equal to another. Unlike equations, which pin down a single value, an inequality defines a whole range of values that satisfy a condition. From budgeting constraints to engineering tolerances, inequalities model any situation where limits apply rather than exact targets.

This lesson covers the four inequality symbols, how to represent solution sets on a number line using open and closed circles, and how to solve linear inequalities. You will also learn to shade regions on a Cartesian graph defined by linear inequalities. Higher tier extends into quadratic inequalities and harder region problems.

Ebumnobi

Understand and use the inequality symbols
Understand and use the convention for open and closed intervals on a number line
Solve simple linear inequalities in one variable and represent the solution set on a number line
Represent simple linear inequalities on rectangular Cartesian graphs
Identify regions on rectangular Cartesian graphs defined by simple linear inequalities
[Higher] Solve quadratic inequalities in one unknown and represent the solution set on a number line
[Higher] Identify harder examples of regions defined by linear inequalities

Akọmọ Ojú-ẹkọ

A theme park sign reads 'You must be at least 140 cm tall to ride'. Translated into algebra this becomes \(h \geq 140\), an inequality. Unlike an equation, which has one answer, this statement is true for every height from 140 cm upwards. Inequalities crop up whenever a rule sets a boundary rather than an exact value.

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Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Inequalities. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

Solve 3x + 2 > 14. A) x > 4 B) x > 6 C) x > 3 D) x < 4 Answer: A
Which number line correctly shows x <= 3? A) Open circle at 3, arrow right B) Filled circle at 3, arrow left C) Open circle at 3, arrow left D) Filled circle at 3, arrow right Answer: B
Solve -2x > 6. A) x > -3 B) x < -3 C) x > 3 D) x < 3 Answer: B
Which integers satisfy -1 < x <= 3? A) -1, 0, 1, 2, 3 B) 0, 1, 2, 3 C) 0, 1, 2 D) -1, 0, 1, 2 Answer: B
On a graph, the region below the line y = 2x + 1 (not including the line) is described by: A) y >= 2x + 1 B) y <= 2x + 1 C) y > 2x + 1 D) y < 2x + 1 Answer: D