Question

solve the following equations. some equations will have a single answer, others will have no solution, and still others will have infinite solutions.

1. $2x + 2x + 2 = 4x + 2$
2. $3(x - 1) = 2x + 9$
3. $2x + 8 = 2(x + 4)$

Explanation:

Step1: Combine like terms (left side)

$2x + 2x + 2 = 4x + 2$

Step2: Simplify and compare sides

$4x + 2 = 4x + 2$
Subtract $4x + 2$ from both sides: $0 = 0$

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Step1: Expand left side of equation

$3(x-1) = 3x - 3$

Step2: Isolate variable terms

$3x - 3 = 2x + 9$
Subtract $2x$ from both sides: $x - 3 = 9$

Step3: Solve for $x$

Add 3 to both sides: $x = 9 + 3 = 12$

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Step1: Expand right side of equation

$2(x+4) = 2x + 8$

Step2: Simplify and compare sides

$2x + 8 = 2x + 8$
Subtract $2x + 8$ from both sides: $0 = 0$

Answer:

1. Infinite solutions
2. $x = 12$
3. Infinite solutions