Simplify the expression: $10-5x+x+3x$

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01-11-2026
Mathematics

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Simplify the expression: $10-5x+x+3x$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-01T19:18:03-05:00

Identify the terms in the expression: $10$, $-5x$, $x$, and $3x$.
Group the like terms containing $x$: $-5x + x + 3x$.
Sum the coefficients of the $x$ terms: $-5 + 1 + 3 = -1$.
Combine the constant and the $x$ term to get the simplified result: $\boxed{10 - x}$.

Explanation

Analysis of the Expression

The objective is to simplify the algebraic expression $10 - 5x + x + 3x$. This involves identifying and combining like terms. Like terms are terms that have the same variable part (in this case, the variable $x$) raised to the same power. Constant terms, like 10, are also considered like terms.

Identifying and Grouping Like Terms

First, we list all the individual terms in the expression: $10$, $-5x$, $x$, and $3x$. Note that $x$ can be written as $1x$. We group the terms containing the variable $x$ together: $-5x + 1x + 3x$. We also have the constant term $10$.

Combining the Coefficients

Now we combine the coefficients of the $x$ terms: $-5 + 1 + 3$.
Calculating this sum:
$-5 + 1 = -4$
$-4 + 3 = -1$
So, $-5x + 1x + 3x = -1x$, which is simply $-x$.

Final Simplified Form

Finally, we combine the resulting term with the constant term to write the simplified expression:
$10 + (-x) = 10 - x$.
Thus, the expression $10 - 5x + x + 3x$ simplifies to $10 - x$.

Examples

Simplifying expressions is a fundamental skill in algebra used for balancing equations, managing budgets, and optimizing designs. For example, if you are calculating the total cost of an item that has a base price of \$10, and you have various discounts or charges involving a variable (like the quantity $x$) such as $-5x$, $x$, and $3x$, simplifying the expression $10 - 5x + x + 3x$ helps you quickly understand the net effect of these changes as $10 - x$. This allows you to easily compute the final cost for any given quantity.