Question

tell whether each equation has no solutions, exactly one solution, or infinitely many solutions.
no solutions\texactly one solution\tinfinitely many solutions
3(x - 7) = 5x + 9\t○\t○\t○
3x - 4 = 3(x + 1)\t○\t○\t○
3x + 1 = 3(x + 2)\t○\t○\t○
submit
work it out

Explanation:

Step1: Analyze \( 3(x - 7)=5x + 9 \)

Expand left side: \( 3x-21 = 5x + 9 \)
Subtract \( 3x \): \( -21=2x + 9 \)
Subtract \( 9 \): \( -30 = 2x \)
Divide by \( 2 \): \( x=-15 \) → exactly one solution.

Step2: Analyze \( 3x - 4 = 3(x + 1) \)

Expand right side: \( 3x-4 = 3x + 3 \)
Subtract \( 3x \): \( -4 = 3 \) → false, no solutions.

Step3: Analyze \( 3x + 1 = 3(x + 2) \)

Expand right side: \( 3x + 1 = 3x + 6 \)
Subtract \( 3x \): \( 1 = 6 \) → false, no solutions.

Answer:

• \( 3(x - 7)=5x + 9 \): exactly one solution (select the "exactly one solution" column for this row)
• \( 3x - 4 = 3(x + 1) \): no solutions (select the "no solutions" column for this row)
• \( 3x + 1 = 3(x + 2) \): no solutions (select the "no solutions" column for this row)