Modulus Equations
Akopọ
The modulus, or absolute value, of a number is its distance from zero, so it is never negative. That single idea, distance, is the key to solving every modulus equation. Strip away the bars and you are left with two ordinary equations to consider, one for each sign.
In this lesson you will solve equations of the form \(|ax+b|=c\), \(|ax+b|=cx+d\) and \(|ax+b|=|cx+d|\). The guiding rule is simple: if \(|\text{something}|=c\) then that something is \(+c\) or \(-c\). You will also learn the vital habit of checking your solutions, because the modulus can quietly create answers that do not work.
Awọn Afojusun
- Solve equations involving the modulus, such as |ax + b| = c, |ax + b| = cx + d and |ax + b| = |cx + d|, using algebraic or graphical methods.
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Oriire fun ipari ẹkọ lori Modulus Equations. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
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- Solve |2x - 1| = 5. A. x = 3 or x = -2 B. x = 2 or x = -3 C. x = 3 only D. x = -2 only Answer: A
- The equation |A| = c (with c >= 0) is equivalent to: A. A = c only B. A = c or A = -c C. A = -c only D. A = 0 Answer: B
- Which value is never possible for |x|? A. 0 B. 5 C. -3 D. 2.5 Answer: C
- Solve |x - 1| = |2x + 1|. A. x = -2 or x = 0 B. x = 2 or x = 0 C. x = 1 or x = -1 D. x = -2 only Answer: A
- When solving |x - 2| = 2x - 7, x = 3 is rejected because: A. it does not solve case 2 B. it makes the right-hand side negative C. it makes |x - 2| negative D. it is not an integer Answer: B
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