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A. Given; B. multiplication; C. distributive; D. collect terms; E. addition; F. division
You are expected to compare each line to the previous line and identify the changes. Apart from combining like terms (collecting terms), there are generally only three properties of interest: distributive property, addition property, multiplication property. Of course, subtraction and division are just addition and multiplication using the appropriate (additive, multiplicative) inverse.
The distributive property involves adding or deleting parentheses, so it is easy to identify.
If terms disappear, it can be due to terms being combined, or due to addition/subtraction. If coefficients disappear, it will generally be due to multiplication/division.
-2.5(-2-3x)+2.5(-4x-1) = -2x -4x . . . . Given
-5(-2 -3x) +5(-4x -1) = -4x -8x . . . . multiplication by 2 (fractions eliminated)
10 +15x -20x -5 = -4x -8x . . . . distributive property (eliminate parentheses)
-5x +5 = -12x . . . . collect terms
5 = -7x . . . . addition of 5x (-5x term disappeared)
-5/7 = x . . . . division by -7 (x coefficient of -7 disappeared)
d. millimeters per hour.
we are given that,
carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.
since, according to the options, we see that,
water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.
we get that, the water can be measured by 'millimeters per hour'.
hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.