Question

the steps to solve an equation are justified by properties of equality. they ensure that the equations stays balanced in order to solve for the missing variable.

• addition property of equality
• subtraction property of equality
• multiplication property of equality
• division property of equality
• distributive property

directions: identify which property justifies each step used to solve the equations below.

1

equation steps	properties/reasons
2. $2x - 18 = -10$	2.
3. $2x = 8$	3.
4. $x = 4$	4.

2

equation steps	properties/reasons
2. $\frac{m}{-3} = -11$	2.
3. $m = 33$	3.

3

equation steps	properties/reasons
2. $5y - 1 = 14$	2.
3. $5y = 15$	3.
4. $y = 3$	4.

Explanation:

Step1: Match step 2 (Equation 1)

The left side expands $2(x-9)$ to $2x-18$ using the rule that $a(b-c)=ab-ac$.
Property: Distributive Property

Step2: Match step 3 (Equation 1)

18 is added to both sides of $2x-18=-10$ to get $2x=8$.
Property: Addition Property of Equality

Step3: Match step 4 (Equation 1)

Both sides of $2x=8$ are divided by 2 to get $x=4$.
Property: Division Property of Equality

Step4: Match step 2 (Equation 2)

10 is subtracted from both sides of $\frac{m}{-3}+10=-1$ to get $\frac{m}{-3}=-11$.
Property: Subtraction Property of Equality

Step5: Match step 3 (Equation 2)

Both sides of $\frac{m}{-3}=-11$ are multiplied by -3 to get $m=33$.
Property: Multiplication Property of Equality

Step6: Match step 2 (Equation 3)

Both sides of $\frac{5y-1}{2}=7$ are multiplied by 2 to get $5y-1=14$.
Property: Multiplication Property of Equality

Step7: Match step 3 (Equation 3)

1 is added to both sides of $5y-1=14$ to get $5y=15$.
Property: Addition Property of Equality

Step8: Match step 4 (Equation 3)

Both sides of $5y=15$ are divided by 5 to get $y=3$.
Property: Division Property of Equality

Answer:

Equation 1

1. Distributive Property
2. Addition Property of Equality
3. Division Property of Equality

Equation 2

1. Subtraction Property of Equality
2. Multiplication Property of Equality

Equation 3

1. Multiplication Property of Equality
2. Addition Property of Equality
3. Division Property of Equality