3. joe solved the equation 3 + x/2 = 10 and justified each step as shown.

identify joe’s error and fix his mistake.

step / justification

3 + x/2 - 10 given equation

x/2 = 7 multiplication property of equality

x = 14 subtraction property of equality

Joe's answer is justified that his mistake was the property shown to steps 3 and 5 was incorrect but his step3 and step5 are right

That is Step3 : (by using Multiplication Property of Equality )

Step5 :  (by using Subtraction Property of Equality )

The correct properties in steps are given below

Step3 : (by using Subtraction Property of Equality )

Step5 :  (by using Multiplication property of Equality )

This steps and the properties used here are correct.

Step-by-step explanation:

Given equation is

Joe solved the equation as below

Step1 :

Step2 :

Step3 : (by using Multiplication Property of Equality )

Step4 :

Step5 :  (by using Subtraction Property of Equality )

Step6 : Therefore x=14

Joe's answer is justified that his mistake was the property shown to steps3 and 5 was incorrect but his step3 and step5 are right

That is Step3 : (by using Multiplication Property of Equality )

Step5 :  (by using Subtraction Property of Equality )

The corrected properties in steps are given below

Step3 : (by using Subtraction Property of Equality )

Step5 :  (by using Multiplication Property of Equality )

This steps and the properties used here are correct

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629