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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
.

5 answers

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 \(a = 2b - x\).

can you make it less advanced

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 little less advanced

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: \(a = 2b - x\).