Keisha solved the following equation: 4x − 2x + 8 = 6(x + 4) step work justification 1 2x + 8 = 6(x + 4) combine like terms 2 2x + 8 = 6x + 24 associative property of multiplication 3 −4x + 8 = 24 subtraction property of equality 4 −4x = 16 addition property of equality 5 x = −4 division property of equality which step has an incorrect justification?

Remark

The second one. The second step removes the brackets on the right. It uses the distributive property which puts back the common factor that was taken out of the two terms 6x and 24. Quite often the distributive property is useful when presenting a problem to be solved.

The associative property is more of an order thing and that is very useful sometimes as well what it says is that if you have three numbers a + b + c the order which you combine things does not matter.

For example 3 + 4 + 5 could be combined as 3 + 4 = 7;  7 + 5 = 12 or 3 + 5 = 8, 8 + 4 = 12.  

The associative property is useful when adding fractions.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,