Question

matching list
listen
match each equation with its corresponding number of solutions.
$6x - 4 = -4 + 6x$ a. infinite solutions
$4x - 6 = 4x + 3$ b. one solution
$-2x + 4 = -3x + 4$ c. no solution

Explanation:

Step1: Analyze \( 6x - 4 = -4 + 6x \)

Subtract \( 6x \) from both sides: \( 6x - 6x - 4 = -4 + 6x - 6x \), which simplifies to \( -4 = -4 \). This is always true, so there are infinite solutions. Match with a.

Step2: Analyze \( 4x - 6 = 4x + 3 \)

Subtract \( 4x \) from both sides: \( 4x - 4x - 6 = 4x - 4x + 3 \), which simplifies to \( -6 = 3 \). This is never true, so there are no solutions. Match with c.

Step3: Analyze \( -2x + 4 = -3x + 4 \)

Add \( 3x \) to both sides: \( -2x + 3x + 4 = -3x + 3x + 4 \), getting \( x + 4 = 4 \). Subtract 4: \( x = 0 \). There is one solution. Match with b.

Answer:

\( 6x - 4 = -4 + 6x \) - a. infinite solutions
\( 4x - 6 = 4x + 3 \) - c. no solution
\( -2x + 4 = -3x + 4 \) - b. one solution