Question 157·Easy·Equivalent Expressions

Treat the minus sign in front of $(x - 5)$ as multiplying everything inside by $-1$; how does that change each term?

After removing all parentheses, put the $x$ terms together and the constant numbers together, then simplify each group.

In one expression line, type 4(2x - 3) - (x - 5) so Desmos graphs or evaluates this as your reference expression.

On separate lines, type each option: 7x - 7, 7x + 7, 9x - 17, and 9x - 7. You can either compare the graphs or create a table for each expression.

Use a table (click the gear icon and add table) for the original expression and each choice, and compare their $y$-values at several $x$-values (for example, $x=0,1,2$). The correct choice will have the same $y$-value as the original expression for every $x$ you test.

Start with the given expression:

Distribute the 4 to both terms inside the first parentheses:

So the expression becomes:

Think of the minus sign before $(x - 5)$ as multiplying by $-1$.

Distribute $-1$ to both terms inside the parentheses:

Now rewrite the expression without parentheses:

Group $x$ terms together and constant terms together:

• $x$ terms: $8x - x$
• Constant terms: $-12 + 5$

Now simplify each group.

Simplify the grouped terms:

• $8x - x = 7x$
• $-12 + 5 = -7$

So the original expression is equivalent to:

This matches answer choice C) 7x - 7.