Question

Complete the process of solving the equation.
Fill in all the missing terms and select all missing descriptions. Simplify any fractions.
–
2a–3+17a=16a+11
–3=16a+11
Add -2a to both sides
Subtract -2a from both sides
Multiply both sides by -2a
Divide both sides by -2a
Combine like terms
–3=11
Add 16a to both sides
Subtract 16a from both sides
Multiply both sides by 16a
Divide both sides by 16a
Apply the distributive property
–
a=
Add 3 to both sides
Subtract 3 from both sides
Multiply both sides by 3
Divide both sides by 3
Apply the distributive property
a=

Answer 1

Let's go through the equation step-by-step and fill in the missing descriptions and terms.

Starting with the original equation:
\[
-2a - 3 + 17a = 16a + 11
\]

We can simplify the left side:
Combine like terms:
\[
(-2a + 17a) - 3 = 16a + 11
\]
This results in:
\[
15a - 3 = 16a + 11
\]

Next, we will isolate \( a \):

1. **Add 3 to both sides**:
\[
15a - 3 + 3 = 16a + 11 + 3
\]
Simplifying gives:
\[
15a = 16a + 14
\]

2. **Subtract 16a from both sides**:
\[
15a - 16a = 16a + 14 - 16a
\]
This simplifies to:
\[
-a = 14
\]

3. **Multiply both sides by -1**:
\[
-a \cdot (-1) = 14 \cdot (-1)
\]
Which yields:
\[
a = -14
\]

So, the final solution is:
\[
a = -14
\]

Now, let's compile the missing descriptions:

**Missing Descriptions**:
1. Combine like terms
2. Add 3 to both sides
3. Subtract 16a from both sides
4. Multiply both sides by -1

Putting it all together, here's the complete solution flow:

1. Combine like terms:
\[
15a - 3 = 16a + 11
\]

2. Add 3 to both sides:
\[
15a = 16a + 14
\]

3. Subtract 16a from both sides:
\[
-a = 14
\]

4. Multiply both sides by -1:
\[
a = -14
\]

Thus:
**Final answer**:
\[
a = -14
\]