Question

Caitlyn needs to solve the equation: 2(3x+1)=3(2-x). after copying the problem correctly she uses the Properties of Algebra to solve for x in 5 steps. There is a reason the justifies each step. What is the justification that Caitlyn used for each step? Name each Property of Algebra.

Step 1 6x + 2 = 6 - 3x
Step 2 2 = 6 - 9x
Step 3 -4 = -9x
Step 4 4/9 = x
Step 5 x = 4/9

Answer 1

See below.

Explanation:

Step 1 6x + 2 = 6 - 3x Distributive property of multiplication over addition

Step 2 2 = 6 - 9x Subtraction property of equality

Step 3 -4 = -9x Subtraction property of equality

Step 4 4/9 = x Division property of equality

Step 5 x = 4/9 Symmetric property of equality

Answer 2

x=49

Explanation:

2(3x+1)=3(2−x)

Step 1: Simplify both sides of the equation.

2(3x+1)=3(2−x)

(2)(3x)+(2)(1)=(3)(2)+(3)(−x)(Distribute)

6x+2=6+−3x

6x+2=−3x+6

Step 2: Add 3x to both sides.

6x+2+3x=−3x+6+3x

9x+2=6

Step 3: Subtract 2 from both sides.

9x+2−2=6−2

9x=4

Step 4: Divide both sides by 9.

9x9=49

x=49