Solve for A 3A-7=17

Solution:

Step 1: Isolate the variable term

Shift all constants to the opposite side of the equation from the variable $A$.

Step 1.1: Add $7$ to both sides

To isolate $A$, add $7$ to both sides, resulting in $3A = 17 + 7$.

Step 1.2: Combine like terms

Combine the constants on the right side: $3A = 24$.

Step 2: Solve for the variable

To find the value of $A$, divide the equation by the coefficient of $A$.

Step 2.1: Divide by the coefficient of $A$

Divide both sides of $3A = 24$ by $3$ to get $\frac{3A}{3} = \frac{24}{3}$.

Step 2.2: Simplify the equation

Reduce the equation to its simplest form.

Step 2.2.1: Eliminate common factors

Remove the common factor of $3$ in $\frac{3A}{3} = \frac{24}{3}$.

Step 2.2.1.1: Simplify the left side

After canceling the $3$s, we have $A = \frac{24}{3}$.

Step 2.2.1.2: Express $A$ as a simplified fraction

The variable $A$ is now alone, and we have $A = \frac{24}{3}$.

Step 2.3: Finalize the solution

Calculate the value of the right side of the equation.

Step 2.3.1: Divide $24$ by $3$

The final step gives us the solution: $A = 8$.

Knowledge Notes:

To solve a linear equation for a variable, we follow a systematic approach:

1. Isolate the variable: We want to get the variable by itself on one side of the equation. This often involves moving terms that do not contain the variable to the other side using addition or subtraction.

2. Combine like terms: If there are similar terms on the same side of the equation, we combine them to simplify the equation.

3. Divide by the coefficient: If the variable has a coefficient (a number it is multiplied by), we divide the entire equation by that coefficient to solve for the variable.

4. Simplify the equation: This involves canceling out common factors and reducing fractions if necessary to get the simplest form of the variable.

5. Check the solution: It's often a good practice to check your solution by plugging it back into the original equation to ensure that it satisfies the equation.

In the given problem, we use these steps to solve for $A$ in the equation $3A - 7 = 17$. The solution involves basic algebraic manipulations such as addition, subtraction, multiplication, and division. Understanding how to manipulate equations and solve for variables is a fundamental skill in algebra.