Mathematics - International - 0607 CIE

Inequalities

Gbogbo ọrọ náà

An inequality says that one quantity is less than, or greater than, another, rather than exactly equal. Speed limits, minimum ages, budget ceilings and safe ranges are all inequalities, and they describe the world far more often than tidy equalities do.

In this lesson you will represent inequalities on a number line, then at Extended level construct and solve linear inequalities, solve them with a graphic display calculator, and picture linear inequalities in two variables as regions on a graph. You will also learn to read off the inequalities that define a shaded region.

Ebumnobi

Represent and interpret inequalities, including on a number line.
Construct, solve and interpret linear inequalities. (Extended only)
Solve inequalities using a graphic display calculator. (Extended only)
Represent and interpret linear inequalities in two variables graphically. (Extended only)
List inequalities that define a given region. (Extended only)

Akọmọ Ojú-ẹkọ

Real limits are rarely a single number; they are ranges. You must be at least a certain height for a ride, spend no more than a budget, keep a temperature within safe bounds. Inequalities are how mathematics captures these everyday constraints, and the same ideas underpin optimisation, the art of getting the best result within limits.

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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 - 4 < 11. A. x < 5 B. x > 5 C. x < 7 D. x > 7 Answer: A
Solve -2x >= 6. A. x >= 3 B. x <= 3 C. x >= -3 D. x <= -3 Answer: D
On a number line, which circle marks a value that is included, as in x >= 2? A. an open circle B. a filled circle C. an arrow only D. a dashed circle Answer: B
When drawing the region for y < 2x + 1, the boundary line should be: A. solid B. dashed C. dotted and shaded D. omitted Answer: B
Is the origin (0, 0) in the region y < 2x + 1? A. Yes B. No C. Only on the line D. Cannot tell Answer: A