What is the solution for a in the equation 2/3 a - 5 = 9?

What is the solution for a in the equation 2/3 a - 5 = 9?

• A. 15
• B. 21
• C. 9
• D. 18

Answer: (B)

To solve the equation \( \frac{2}{3} a - 5 = 9 \), we will first isolate the term containing \( a \). 1. Start by adding 5 to both sides of the equation to eliminate the constant term on the left side. This gives us: \[ \frac{2}{3} a - 5 + 5 = 9 + 5 \] \[ \frac{2}{3} a = 14 \] 2. The next step to solve for \( a \) is to get rid of the fraction. To do this, multiply both sides of the equation by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \): \[ a = 14 \times \frac{3}{2} \] 3. Now, perform the multiplication: \[ a = 14 \times \frac{3}{2} = \frac{42}{2} = 21 \] Thus, the solution for \( a \) is 21, confirming that the correct choice aligns with the calculations where we systematically isolated \( a \) through basic algebraic operations.

To solve the equation ( \frac{2}{3} a - 5 = 9 ), we will first isolate the term containing ( a ).

1. Start by adding 5 to both sides of the equation to eliminate the constant term on the left side. This gives us:

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

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

2. The next step to solve for ( a ) is to get rid of the fraction. To do this, multiply both sides of the equation by the reciprocal of ( \frac{2}{3} ), which is ( \frac{3}{2} ):

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

3. Now, perform the multiplication:

[ a = 14 \times \frac{3}{2} = \frac{42}{2} = 21 ]

Thus, the solution for ( a ) is 21, confirming that the correct choice aligns with the calculations where we systematically isolated ( a ) through basic algebraic operations.