Math Is Fun Forum

simone

Member

Registered: 2007-10-05

Posts: 19

urgent help please-absolute value notation-first degreeinequalities

If y>=0 , what is the value of x?

1) |x-3|>=y

2) |x-3|<=-y

A) Statement 1) alone is sufficient
B) Statement 2) alone is sufficient
C) Statements 1) and 2) together are sufficient
D) Each statement alone is sufficient
E) Statement 1) and 2) together are not sufficient

the excercise book I'm using gives B) as correct answer, could you explain the reasoning behind it?
thank you

Last edited by simone (2007-10-12 21:25:26)

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: urgent help please-absolute value notation-first degreeinequalities

Look at statement (2). Remember that y is either greater than, or equal to, zero (by the question).

If y were greater than zero, the inequality wouldn't make sense: it'd be trying to tell you that a positive number (the modulus expression, LHS) is less than a negative number.

The only option, therefore, is that y = 0, and therefore | x - 3 | = 0, thus x = 3.

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Bad speling makes me [sic]

simone

Member

Registered: 2007-10-05

Posts: 19

Re: urgent help please-absolute value notation-first degreeinequalities

thank you so much! very clear and sound!
would you take a look at the other question I posted?
thank you