Dame ejemplos de ecuaciones lineales de dos pasos.
Understand the Problem
La pregunta solicita ejemplos de ecuaciones lineales que se resuelven en dos pasos. Esto significa proporcionar ecuaciones donde la variable se aísla usando dos operaciones algebraicas (como suma/resta y multiplicación/división).
Answer
1. $2x + 3 = 7$, $x = 2$ 2. $3x - 5 = 10$, $x = 5$
Answer for screen readers
Here are two examples of linear equations that can be solved in two steps:
- $2x + 3 = 7$, solution: $x = 2$
- $3x - 5 = 10$, solution: $x = 5$
Steps to Solve
- Choose a variable and its coefficient
Let's choose $x$ as the variable and 2 as its coefficient. So far we have $2x$.
- Add or subtract a constant
Let's add 3 to the term $2x$. Now we have $2x + 3$.
- Set the expression equal to a value
Let's set $2x + 3$ equal to 7. The equation is $2x + 3 = 7$.
- Solve the equation
First, subtract 3 from both sides of the equation: $2x + 3 - 3 = 7 - 3$, which simplifies to $2x = 4$.
- Isolate the variable
Divide both sides of the equation by 2: $\frac{2x}{2} = \frac{4}{2}$, which simplifies to $x = 2$.
- Provide another example
Let's create another equation: $3x - 5 = 10$
- Solve this equation
Add 5 to both sides: $3x - 5 + 5 = 10 + 5$, which simplifies to $3x = 15$.
- Isolate the variable
Divide both sides by 3: $\frac{3x}{3} = \frac{15}{3}$, which simplifies to $x = 5$.
Here are two examples of linear equations that can be solved in two steps:
- $2x + 3 = 7$, solution: $x = 2$
- $3x - 5 = 10$, solution: $x = 5$
More Information
These equations are called "two-step equations" because solving them requires exactly two algebraic steps to isolate the variable.
Tips
A common mistake is performing the operations in the wrong order. For example, in the equation $2x + 3 = 7$, one might try to divide by 2 before subtracting 3. Remember to reverse the order of operations (PEMDAS/BODMAS) when solving for the variable.
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