Question

marco and kim solve the equation 3(x + 1) = 2x. marco’s solution is, x = -3. kim’s solution is x = 3. which is correct? explain.

Explanation:

Step1: Expand left-hand side

$3(x+1) = 3x + 3$

Step2: Rewrite original equation

$3x + 3 = 2x$

Step3: Isolate x terms

$3x - 2x = -3$

Step4: Simplify to solve for x

$x = -3$

Step5: Verify Marco's solution

Substitute $x=-3$ into original equation:
Left-hand side: $3(-3+1)=3(-2)=-6$
Right-hand side: $2(-3)=-6$
Both sides are equal.

Step6: Verify Kim's solution

Substitute $x=3$ into original equation:
Left-hand side: $3(3+1)=3(4)=12$
Right-hand side: $2(3)=6$
Sides are not equal.

Answer:

Marco's solution $x=-3$ is correct. When solving the equation, expanding and isolating $x$ gives $x=-3$, and substituting this value back into the original equation confirms both sides are equal, while Kim's solution does not satisfy the equation.