First simplify $4(2x - 3)$, then simplify $3(1 - 2x)$. Write each result separately before adding them.

After expanding, group the $x$-terms together and the constant numbers together. Be careful with negative signs when you add them.

In Desmos, type y = 4(2x - 3) + 3(1 - 2x) to graph the line that represents the original expression.

On new lines, type each choice as a separate function, for example:

• y = 14x - 9
• y = 2x + 6
• y = -2x - 9
• y = 2x - 9 so that all four answer-choice lines appear on the graph.

Look at the graph of the original expression and see which answer-choice line lies exactly on top of it for all $x$-values. The choice whose line perfectly overlaps the original graph is the equivalent expression.

The expression $4(2x - 3) + 3(1 - 2x)$ has parentheses with numbers (coefficients) in front.

To simplify it, you should use the distributive property on each set of parentheses, then combine like terms.

Apply the distributive property to $4(2x - 3)$:

• Multiply $4$ by $2x$ to get $8x$.
• Multiply $4$ by $-3$ to get $-12$.

So $4(2x - 3)$ becomes $8x - 12$.

Now apply the distributive property to $3(1 - 2x)$:

• Multiply $3$ by $1$ to get $3$.
• Multiply $3$ by $-2x$ to get $-6x$.

So $3(1 - 2x)$ becomes $3 - 6x$.

Now add the two results together:

Group like terms:

• $x$-terms: $8x - 6x = 2x$
• Constant terms: $-12 + 3 = -9$

So the simplified, equivalent expression is $2x - 9$.