Which property of equality justifies the step for solving the equation that is displayed?
3z2−5=10
3z2−5+5=10+5
3z2=15
(1 point)
Responses
Addition Property of Equality
Addition Property of Equality
Division Property of Equality
Division Property of Equality
Subtraction Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Multiplication Property of Equality
How many solutions will the equation 23(6m+9)−6=4m have?(1 point)
Responses
infinite/many solutions
infinite/many solutions
one solution
one solution
no solution
no solution
two solutions
one solution
Identify the pair of linear equations that have the same solution set.(1 point)
Responses
4=k2+5 and 4j−143+5=3
4k−5=2k and 8j−2=3j
3(m+1)=10 and 6n+3=6−n
2(3g+5)−2g=2(4−g) and −36h6=2
2(3g+5)−2g=2(4−g) and −36h6=2
Subtraction Property of Equality
The property of equality that justifies the step for solving the equation is the Addition Property of Equality. This property states that if you add the same number to both sides of an equation, the equation remains true.
In the given equation 3z^2 - 5 = 10, we want to isolate the variable z^2. To do this, we can get rid of the -5 on the left side by adding 5 to both sides of the equation.
3z^2 - 5 + 5 = 10 + 5
Simplifying both sides:
3z^2 = 15
By adding 5 to both sides of the equation, we are following the Addition Property of Equality, which allows us to maintain the equality of the equation.