Give two examples of each type of number: real, natural, integers, rational and irrational. Explain step-by-step how to simplify -5(2x – 3y + 6z – 10)

9514 1404 393

Step-by-step explanation:

A) Any positive integer is all of real, natural, integer, and rational. A couple of examples of positive integers are 2, and 3.

Any non-complex number is real: -98.6, +29.7π.

Natural numbers are positive integers: 89, 10103.

Integers are any positive or negative number that has no fractional part. Zero is also an integer. A couple are -3, 0.

A rational number is one that can be expressed as the ratio of two integers. Any finite decimal number and any repeating decimal number are rational numbers. A couple of these are 22/7 and -0.0037285.

An irrational number is a number that cannot be expressed as the ratio of two integers. A cube root of a number that is not a perfect cube will be irrational, for example, The same is true of other roots. √2, ∛-5 are irrational. Pi (π) is a famous irrational number, along with 'e', the base of natural logarithms.

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B) The terms inside parentheses are unlike, so cannot be combined. The only way this expression can be simplified is by removing the parentheses using the distributive property.

  -5(2x -3y +6z -10) = (-5)(2x) +(-5)(-3y) +(-5)(6z) +(-5)(-10)

  = -10x +15y -30z +50

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