Solve for the value of the variable: $5x + 12 - 6x = 5x - 48$

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03-11-2026
Mathematics

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Solve for the value of the variable: $5x + 12 - 6x = 5x - 48$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T14:45:49-05:00

Simplify the left-hand side of the equation by combining like terms to get $-x + 12 = 5x - 48$.
Isolate the variable term by adding $x$ to both sides: $12 = 6x - 48$.
Move the constant term to the other side by adding $48$ to both sides: $60 = 6x$.
Divide by 6 to find the solution: $x = \boxed{10}$.

Explanation

Problem Analysis and Objective

The goal is to solve for the variable $x$ in the equation $5x + 12 - 6x = 5x - 48$. This is a linear equation in one variable, which means our objective is to isolate $x$ by simplifying both sides of the equation and using algebraic operations to move terms involving $x$ to one side and constant terms to the other.

Simplifying the Equation

First, we simplify the left-hand side by combining the like terms $5x$ and $-6x$. We have:
\[(5x - 6x) + 12 = 5x - 48\]
\[-x + 12 = 5x - 48\]

Isolating the Variable Term

Next, we gather all the terms containing $x$ on the right-hand side by adding $x$ to both sides of the equation:
\[12 = 5x + x - 48\]
\[12 = 6x - 48\]

Isolating the Constant Term

Now, we move the constant term $-48$ to the left-hand side by adding $48$ to both sides:
\[12 + 48 = 6x\]
\[60 = 6x\]

Final Solution

Finally, to solve for $x$, we divide both sides by the coefficient of $x$, which is $6$:
\[x = \frac{60}{6}\]
\[x = 10\]
By substituting $x = 10$ back into the original equation, we get $5(10) + 12 - 6(10) = 50 + 12 - 60 = 2$ on the left side and $5(10) - 48 = 50 - 48 = 2$ on the right side. Since both sides are equal, the solution is correct. The final value of $x$ is $\boxed{10}$.

Examples

Solving linear equations is a fundamental skill in algebra used in everyday scenarios. For example, imagine you are comparing two service plans: Plan A charges a base fee of $\$12$ plus a rate, while Plan B is a different rate minus a one-time discount. By modeling these as an equation like $5x + 12 - 6x = 5x - 48$, you can find the specific usage level $x$ where both plans result in the same total cost, allowing you to make an informed financial decision.