Question
The following equation is an example of a literal equation.
2(x+a) =4b
A. Solve the given equation for the variable a In your final answer, include all of your work.
B. In two or more complete sentences, explain the specific process that you followed in solving for a
.
2(x+a) =4b
A. Solve the given equation for the variable a In your final answer, include all of your work.
B. In two or more complete sentences, explain the specific process that you followed in solving for a
.
Answers
GPT-4o mini
Let's solve the equation \(2(x + a) = 4b\) for the variable \(a\).
### A. Solve the equation for \(a\):
1. **Start with the given equation**:
\[
2(x + a) = 4b
\]
2. **Divide both sides by 2** to simplify the equation:
\[
x + a = \frac{4b}{2}
\]
\[
x + a = 2b
\]
3. **Isolate \(a\)** by subtracting \(x\) from both sides:
\[
a = 2b - x
\]
Thus, the solution for \(a\) is:
\[
\boxed{a = 2b - x}
\]
---
### B. Explanation of the process:
In solving for \(a\), I began with the equation \(2(x + a) = 4b\) and applied algebraic operations to isolate the variable \(a\). First, I divided both sides of the equation by 2 to eliminate the coefficient in front of the parentheses. This step simplified the equation and allowed me to express the sum \(x + a\) as \(2b\). Finally, to solve for \(a\), I rearranged the equation by subtracting \(x\) from both sides, which yielded the final expression \(a = 2b - x\).
### A. Solve the equation for \(a\):
1. **Start with the given equation**:
\[
2(x + a) = 4b
\]
2. **Divide both sides by 2** to simplify the equation:
\[
x + a = \frac{4b}{2}
\]
\[
x + a = 2b
\]
3. **Isolate \(a\)** by subtracting \(x\) from both sides:
\[
a = 2b - x
\]
Thus, the solution for \(a\) is:
\[
\boxed{a = 2b - x}
\]
---
### B. Explanation of the process:
In solving for \(a\), I began with the equation \(2(x + a) = 4b\) and applied algebraic operations to isolate the variable \(a\). First, I divided both sides of the equation by 2 to eliminate the coefficient in front of the parentheses. This step simplified the equation and allowed me to express the sum \(x + a\) as \(2b\). Finally, to solve for \(a\), I rearranged the equation by subtracting \(x\) from both sides, which yielded the final expression \(a = 2b - x\).
can you make it less advanced
GPT-4o mini
Sure! Let’s simplify the explanation and the steps to solve the equation for \(a\).
### A. Solve the equation for \(a\):
1. **Start with the equation**:
\[
2(x + a) = 4b
\]
2. **Divide both sides by 2** to make it simpler:
\[
x + a = \frac{4b}{2}
\]
\[
x + a = 2b
\]
3. **Now, to get \(a\) alone**, subtract \(x\) from both sides:
\[
a = 2b - x
\]
So, the final answer is:
\[
\boxed{a = 2b - x}
\]
---
### B. Explanation of the process:
To solve for \(a\), I started with the equation \(2(x + a) = 4b\). First, I divided both sides by 2 to simplify it, making it easier to work with. Then, I wanted to get \(a\) by itself, so I subtracted \(x\) from both sides. This left me with the equation \(a = 2b - x\). This way, I found the value of \(a\).
### A. Solve the equation for \(a\):
1. **Start with the equation**:
\[
2(x + a) = 4b
\]
2. **Divide both sides by 2** to make it simpler:
\[
x + a = \frac{4b}{2}
\]
\[
x + a = 2b
\]
3. **Now, to get \(a\) alone**, subtract \(x\) from both sides:
\[
a = 2b - x
\]
So, the final answer is:
\[
\boxed{a = 2b - x}
\]
---
### B. Explanation of the process:
To solve for \(a\), I started with the equation \(2(x + a) = 4b\). First, I divided both sides by 2 to simplify it, making it easier to work with. Then, I wanted to get \(a\) by itself, so I subtracted \(x\) from both sides. This left me with the equation \(a = 2b - x\). This way, I found the value of \(a\).
a little less advanced
GPT-4o mini
Of course! Let's make it even simpler.
### A. Solve the equation for \(a\):
1. **Start with the original equation**:
\[
2(x + a) = 4b
\]
2. **Divide both sides by 2** to make it simpler:
\[
x + a = 2b
\]
3. **Now, to find \(a\)**, subtract \(x\) from both sides:
\[
a = 2b - x
\]
So, the answer is:
\[
\boxed{a = 2b - x}
\]
---
### B. Explanation of the process:
To find \(a\), I started with the equation \(2(x + a) = 4b\). First, I divided both sides by 2 to make it easier to understand. Then, I took away \(x\) from both sides so that I could get \(a\) by itself. That led me to the final answer: \(a = 2b - x\).
### A. Solve the equation for \(a\):
1. **Start with the original equation**:
\[
2(x + a) = 4b
\]
2. **Divide both sides by 2** to make it simpler:
\[
x + a = 2b
\]
3. **Now, to find \(a\)**, subtract \(x\) from both sides:
\[
a = 2b - x
\]
So, the answer is:
\[
\boxed{a = 2b - x}
\]
---
### B. Explanation of the process:
To find \(a\), I started with the equation \(2(x + a) = 4b\). First, I divided both sides by 2 to make it easier to understand. Then, I took away \(x\) from both sides so that I could get \(a\) by itself. That led me to the final answer: \(a = 2b - x\).