Question

solve 15 - 5a = 2(6 - 3a)
options:
○ a = -3
○ a = 2
○ a = 3
○ a = -2

Explanation:

Step1: Expand the right side

We start with the equation \(15 - 5a = 2(6 - 3a)\). First, we use the distributive property to expand the right - hand side. The distributive property states that \(c(a + b)=ca+cb\), so \(2(6 - 3a)=2\times6-2\times3a = 12-6a\). Our equation becomes \(15 - 5a=12 - 6a\).

Step2: Add \(6a\) to both sides

To get all the \(a\) terms on one side, we add \(6a\) to both sides of the equation. \((15 - 5a)+6a=(12 - 6a)+6a\). Simplifying both sides: \(15 - 5a+6a=12-6a + 6a\), which gives \(15 + a=12\).

Step3: Subtract 15 from both sides

Now, we want to solve for \(a\). We subtract 15 from both sides of the equation \(15 + a=12\). \((15 + a)-15=12 - 15\). Simplifying, we get \(a=12 - 15=- 3\)? Wait, no, wait. Wait, let's re - check step 2. Wait, \(15-5a + 6a=15 + a\), and \(12-6a + 6a = 12\). Then \(15 + a=12\), subtract 15: \(a=12 - 15=-3\)? But let's check again. Wait, the original equation is \(15-5a = 2(6 - 3a)\). Expand right side: \(15-5a=12-6a\). Add \(6a\) to both sides: \(15-5a + 6a=12-6a+6a\), so \(15 + a=12\). Subtract 15: \(a=12 - 15=-3\). Wait, but let's verify the solution by plugging \(a = - 3\) back into the original equation. Left side: \(15-5\times(-3)=15 + 15 = 30\). Right side: \(2(6-3\times(-3))=2(6 + 9)=2\times15 = 30\). So \(a=-3\) is correct. Wait, but in the options, \(a = - 3\) is one of the options. Wait, maybe I made a mistake in the sign earlier. Wait, let's go through the steps again carefully.

Original equation: \(15-5a=2(6 - 3a)\)

Step 1: Expand the right - hand side using the distributive property \(a(b - c)=ab-ac\). So \(2(6-3a)=2\times6-2\times3a = 12-6a\). The equation is now \(15-5a=12-6a\).

Step 2: Add \(6a\) to both sides to get: \(15-5a + 6a=12-6a+6a\). Simplify both sides: \(15 + a=12\).

Step 3: Subtract 15 from both sides: \(a=12 - 15=-3\).

Answer:

\(a=-3\) (corresponding to the option with \(a = - 3\))