For each linear equation, indicate whether the equation has no solution, one solution. or infinitely many solutions.

This problem requires you to show your work.

(3 point.
3(x+3)=7+3x+6−x
8(x+2)=5x+16+3x
6x+2−4x=2(x+2)

3 answers

Let's go through each equation step by step.

Expand both sides: \[ 3(x + 3) = 3x + 9 \] \[ 7 + 3x + 6 - x = 3x + 13 - x = 2x + 13 \]

So we rewrite the equation: \[ 3x + 9 = 2x + 13 \]
Get all \(x\) terms on one side and constant terms on the other: \[ 3x - 2x = 13 - 9 \] \[ x = 4 \]

Conclusion: This equation has one solution, \(x = 4\).

Expand both sides: \[ 8(x + 2) = 8x + 16 \] \[ 5x + 16 + 3x = 8x + 16 \]

So we rewrite the equation: \[ 8x + 16 = 8x + 16 \]
Simplifying: \[ 8x + 16 - 8x - 16 = 0 \] \[ 0 = 0 \]

Conclusion: This equation has infinitely many solutions (the two sides are identical).

Combine like terms on the left: \[ 6x - 4x + 2 = 2x + 2 \] \[ 2x + 2 = 2x + 2 \]
Simplifying: \[ 2x + 2 - 2x - 2 = 0 \] \[ 0 = 0 \]

Conclusion: This equation also has infinitely many solutions (the two sides are identical).

hiii

one has to be no answer