Name the property of equality or congruence that justifies going from the first statement to the second statement.
StartFraction x Over 2 EndFraction equals 3x2=3
x equals 6x=6
symmetric property of
congruencesymmetric property of congruence
distributive propertydistributive property
substitution property
multiplication property of
equalitymultiplication property of equality
transitive property of
congruencetransitive property of congruence
symmetric property of
equalitysymmetric property of equality
reflexive property of equality
subtraction property of
equalitysubtraction property of equality
transitive property of equality
division property of equality
addition property of equality
reflexive property of congruence
addition
The property of equality or congruence that justifies going from the first statement to the second statement is the multiplication property of equality.
The property of equality or congruence that justifies going from the first statement "StartFraction x Over 2 EndFraction equals 3" to the second statement "x equals 6" is the division property of equality.
To understand how the division property of equality is used, let's break it down step-by-step:
1. The first statement says "StartFraction x Over 2 EndFraction equals 3". This means that the quantity x divided by 2 is equal to 3.
2. To isolate the variable x on one side of the equation, we can apply the inverse operation of division, which is multiplication.
3. Multiplying both sides of the equation by 2, we get x = 3 * 2 which simplifies to x = 6.
So, the division property of equality allows us to divide both sides of an equation by the same number to solve for the variable and obtain the second statement x = 6.