Solving Equation Proofs

Jared solved the equation shown below. Given: 5(x + 1) - 3(x -2) = 13 Step 1: 5x + 5 - 3x + 6 = 13 Step 2: 5x - 3x + 5 + 6 = 13 Step 3: 2x + 11 = 13 Step 4: 2x + 11 - 11 = 13 - 11 Step 5: 2x = 2 Answer: x = 1 Which properties did he apply from step 1 to step 2?

• Associative pro

• Distributive property

• Subtraction property

• Commutative property

Jill solved the equation below. 2\left(x\ -1\right)\ =\ x\ +12 2x\ -\ 2\ =\ x+12 x-2=\ 12 x=14 She applied three properties of equality: I. Addition property of equality, II. Subtraction property of equality and III. Distributive property. In which order did Jill use the properties?

• I, II, III

• III, I, II

• III, II, I

• I, III, II

Find the error

• Adding 2x to 3x

• Subtracting 5 from both sides

• Adding 2x to -2x

• Dividing by 5 on both sides

What is reason 1?

• Subtraction Property of Equality

• Transitive Property of Equality

• Given

• Prove

Which property of real numbers justifies the work shown from Step 1 to Step 2?

• Distributive Property

• Commutative Property

• Identity Property

• Associative Property

Which property justifies the work in solving this equation?

• Addition Property of Equality

• Additive Inverse Property

• Identity Property of Addition

• Subtraction Property of Equality

Which property of real numbers was used to get from Step 3 to Step 4?

• Addition Property of Equality

• Subtraction Property of Equality

• Additive Inverse Property

• Substitution Property

Which property of real numbers was used to get from Step 3 to Step 4?

• Addition Property of Equality

• Subtraction Property of Equality

• Symmetric Property

• Substitution Property

Which property justifies the work in solving this equation?

• Addition Property of Equality

• Additive Inverse Property

• Identity Property of Addition

• Subtraction Property of Equality

What is step 6

• Subtraction property of equality

• Addition property of equality

• Division property of equality