Question

Solve the following two equations for the variable X using the 2-column proof method:

A) 6(x - 3) + 2^2 = 4x + 10
B) (4x + 1) / 3 = 11

Answer 1

The two-column proof method was used to solve for X in two equations, yielding solutions of X=12 for the first equation and X=8 for the second equation through simple algebraic manipulations.

Step-by-step explanation:

To solve the given equations for the variable X using the two-column proof method, let's proceed step by step.

Equation A: 6(x - 3) + 22 = 4x + 10

1. Distribute 6 into (x - 3): 6x - 18 + 4 = 4x + 10
2. Combine like terms: 6x - 14 = 4x + 10
3. Subtract 4x from both sides: 2x - 14 = 10
4. Add 14 to both sides: 2x = 24
5. Divide both sides by 2: x = 12

Equation B: (4x + 1) / 3 = 11

1. Multiply both sides by 3 to eliminate the denominator: 4x + 1 = 33
2. Subtract 1 from both sides: 4x = 32
3. Divide both sides by 4: x = 8

These steps clearly demonstrate how to solve for X in both equations using straightforward algebraic manipulations, which fall into the category of linear equations and adhere to principles in solving equations.