Question

show what you know
4.05
melanie and kala each started solving the equation \\(\frac{1}{2}(7x - 6) = 6x - 10\\).
melanie
\\(\frac{1}{2}(7x - 6) = 6x - 10\\)
\\(3.5x - 6 = 6x - 10\\)
kala
\\(\frac{1}{2}(7x - 6) = 6x - 10\\)
\\(7x - 6 = 12x - 20\\)
whose move kept the equation balanced? circle one.
melanie’s kala’s both neither
explain your thinking.
how well did you understand the math in this lesson?
reflect on the math from this lesson.

• i can solve an equation where the variable terms appear on both sides of the equal sign.
• i can analyze solving steps to determine if they keep an equation balanced.

how did you feel about this lesson?

Explanation:

Step1: Check Melanie's step

Melanie distributed $\frac{1}{2}$ only to $7x$, not to $-6$. The correct distribution would be $\frac{1}{2}(7x-6)=3.5x - 3$, but she wrote $3.5x - 6$. This unbalances the equation.

Step2: Check Kala's step

Kala multiplied both sides of the equation by 2:
Left side: $2\times\frac{1}{2}(7x-6)=7x-6$
Right side: $2\times(6x-10)=12x-20$
This follows the property of equality (multiplying both sides by the same non-zero number keeps the equation balanced).

of thinking:
To keep an equation balanced, the same operation must be applied to the entire side of the equation. Melanie made an error when distributing $\frac{1}{2}$: she only multiplied $7x$ by $\frac{1}{2}$ to get $3.5x$, but she did not multiply $-6$ by $\frac{1}{2}$ (she left it as $-6$ instead of $-3$), so her step unbalanced the equation. Kala multiplied every term on both sides of the equation by 2, which maintains the equality and keeps the equation balanced.

Answer:

Kala's