Question 34·Easy·Equivalent Expressions

Treat $-(4x - 7)$ as $-1$ times $(4x - 7)$. What does that do to both $4x$ and $-7$?

Once the parentheses are removed, group the $x$-terms together and the constant numbers together, then simplify each group.

In the first line, type y = 3(2x - 5) - (4x - 7) + 6 to represent the original expression as a function.

On new lines, type y = 2x - 2, y = 2x + 2, y = -2x - 2, and y = -2x + 2. Each line will create a different graph.

Use the table feature (click the gear next to an equation and choose "Convert to table") or visually compare the graphs. The correct choice will have a graph that lies exactly on top of the graph of the original expression and will give the same $y$-values as the original for every $x$ you test.

Start by expanding the parentheses.

• For $3(2x - 5)$, distribute $3$:

  • $3 \cdot 2x = 6x$
  • $3 \cdot (-5) = -15$
  • So $3(2x - 5) = 6x - 15$.

• For $-(4x - 7)$, think of distributing $-1$:

  • $-1 \cdot 4x = -4x$
  • $-1 \cdot (-7) = +7$
  • So $-(4x - 7) = -4x + 7$.

Now rewrite the whole expression using these results:

Group the terms with $x$ together and the constant terms together:

• $x$-terms: $6x - 4x$
• Constant terms: $-15 + 7 + 6$

Compute each group separately:

• $6x - 4x = 2x$
• For the constants:

Combine the simplified $x$-term and constant term:

• The expression becomes $2x - 2$.

Now look at the answer choices and select the one that matches $2x - 2$. That is choice A.) $2x - 2$.