Simplifying a linear expression with distribution and combining terms

Key takeaway: This is a standard distributive-property problem: expand the parentheses, combine like terms, and match the result to the correct option.

Identify the operation

We need to simplify

$7x-5(2x-4).$

The main skill is distributing the $-5$ across both terms inside the parentheses. This type of problem is common in algebra because signs often cause mistakes.

Expand carefully

Apply the distributive property:

$-5(2x-4)=-10x+20.$

So the expression becomes

$7x-10x+20.$

Now combine like terms:

$7x-10x=-3x.$

Therefore

$7x-5(2x-4)=-3x+20.$

Match the answer choice

The simplified form is

$\boxed{-3x+20}$

which matches option (a).

Common mistake to avoid

The most common error is forgetting that the minus sign in front of $5(2x-4)$ changes both terms inside the parentheses. If you distribute only to the first term and leave the second as $-4$, you will get the wrong sign on the constant term. Another easy error is combining $7x$ and $20$ as if they were like terms; they are not, because one term has a variable and the other does not.

For this problem, the correct method is direct distribution followed by combining like terms. That gives the final simplified expression quickly and reliably.

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Pitfalls the pros know 👇 Students often expand $-5(2x-4)$ as $-10x-20$ because they ignore the sign change on the second term. The minus in front of the parentheses must be distributed to both terms, so $-5\cdot(-4)$ becomes $+20$, not $-20$. Another issue is rushing through the last step and picking the answer choice that looks most similar to the original expression. The safest approach is to write the intermediate line $7x-10x+20$ before combining terms. That makes the sign pattern clear and prevents careless selection errors.

What if the problem changes? If the expression were changed to $7x-5(2x+4)$, then distribution would give $7x-10x-20=-3x-20$, which would match a different answer choice. If the coefficient in front of the parentheses were positive, such as $7x+5(2x-4)$, the result would be $17x-20$. These variants show that the sign in front of the parentheses is the key feature controlling the final constant term and the coefficient of $x$.

Tags: distributive property, like terms, linear expression