In the equation 2/3 a - 5 = 9, what is the first step to isolate a?

In the equation 2/3 a - 5 = 9, what is the first step to isolate a?

• A. Add 5 to both sides
• B. Multiply both sides by 2
• C. Subtract 5 from both sides
• D. Add 2/3 to both sides

Answer: (A)

To isolate the variable \( a \) in the equation \( \frac{2}{3}a - 5 = 9 \), the first step involves eliminating the constant term on the left side of the equation. This constant term is -5, which we need to remove in order to isolate the term containing \( a \). Adding 5 to both sides of the equation achieves this because it balances the equation, allowing us to work with just the term involving \( a \). Here’s how it looks: Starting with: \[ \frac{2}{3}a - 5 = 9 \] When you add 5 to both sides, the equation becomes: \[ \frac{2}{3}a = 9 + 5 \] \[ \frac{2}{3}a = 14 \] Now, \( \frac{2}{3}a \) is isolated on the left side, which allows you to proceed to the next steps to solve for \( a \). This step is crucial because it simplifies your equation significantly, setting the stage for further manipulation necessary to find the value of \( a \).

To isolate the variable ( a ) in the equation ( \frac{2}{3}a - 5 = 9 ), the first step involves eliminating the constant term on the left side of the equation. This constant term is -5, which we need to remove in order to isolate the term containing ( a ).

Adding 5 to both sides of the equation achieves this because it balances the equation, allowing us to work with just the term involving ( a ). Here’s how it looks:

Starting with:

[ \frac{2}{3}a - 5 = 9 ]

When you add 5 to both sides, the equation becomes:

[ \frac{2}{3}a = 9 + 5 ]

[ \frac{2}{3}a = 14 ]

Now, ( \frac{2}{3}a ) is isolated on the left side, which allows you to proceed to the next steps to solve for ( a ). This step is crucial because it simplifies your equation significantly, setting the stage for further manipulation necessary to find the value of ( a ).