CPM Homework Help : AC Problem 3-67

Paris is trying to solve the equation $3x^2−(2x−4)=3+3x^2+1$ . Her work is partially recorded below. Copy her table and fill in her missing work to solve for $x$ .

Left Expression	Right Expression	Explanation
$3x^2-(2x-4)$	$3+3x^2+1$	Starting expressions.
$3x^2-2x+4$	$3+3x^2+1$
		Remove $3x^2$ from both sides.
$-2x$	$0$
		Divide both sides by $-2$ .

Hint:

To figure out what comes next in the equation, notice what changes in each step and make sure to
read the explanation column.

Answer:

Left Expression	Right Expression	Explanation
$3x^2-(2x-4)$	$3+3x^2+1$	Starting expressions.
$3x^2-2x+4$	$3+3x^2+1$	$\color{red}{\text{Flip tiles from "-" region to "+" region.}}$
$\color{red}{-2x+4}$	$\color{red}{3+1}$	Remove $3x^2$ from both sides.
$-2x$	$0$	$\color{red}{\text{Take 4 away from both sides.}}$
		Divide both sides by $-2$ .