Beth solved the equation by applying the Distributive Property, then Simplifying/Combining Like Terms, using the Subtraction and Addition Properties of Equality, and finally the Division Property of Equality, in order to isolate x and find that x = 5.
Beth used several properties to solve the equation 2(x-3)+12 = 5x - 9. The correct order of the properties she used is as follows:
Distributive Property: To expand the equation to 2x - 6 + 12.
Simplify/Combine Like Terms: To combine -6 and 12 into +6 on the left side of the equation.
Subtraction Property of Equality: To subtract 2x from both sides to get 6 = 3x - 9.
Addition Property of Equality: To add 9 to both sides, getting to 15 = 3x.
Division Property of Equality: To divide both sides by 3, resulting in x = 5.
This sequence of steps allowed Beth to isolate the variable x and solve the equation.
The probable question may be:
Beth solves this equation using the following steps. Use the terms from the word bank to help you write which properties she used to get the solution.
Put the list in order of the properties she used to solve the equation for x.
2(x-3)+12 =5r-9
2x-6+12=5x-9
2r+6=5r-9
6=3x-9
15=3x
5=x
Distributive Property
Subtraction Property of Equality
Simplify/Combine Like Terms
Addition Property of Equality
Division Property of Equality