Question

Simplify the expression:

–2(q − 4) =

Combine any like terms in the expression. If there are no like terms, rewrite the expression.
4+8q+6q

What value of s is a solution to this equation?
4(s–3)–18=
–
26 s=1 s=-2

Which property of equality is shown below?


If:
–40 −
t
=
s
Then:
–79 +
–40 −
t
=
–79 +
s

Answer 1

Let's go through each part step by step.

### 1. Simplify the expression: –2(q − 4)

To simplify \(-2(q - 4)\):
1. Distribute \(-2\) to both \(q\) and \(-4\):
\[
-2(q) + (-2)(-4) = -2q + 8
\]
So, the simplified expression is:
\[
-2q + 8
\]

---

### 2. Combine any like terms in the expression: 4 + 8q + 6q

In the expression \(4 + 8q + 6q\), combine the like terms \(8q\) and \(6q\):
\[
8q + 6q = 14q
\]
Therefore, the expression becomes:
\[
4 + 14q
\]

---

### 3. Find a value of \(s\) that is a solution to the equation: 4(s - 3) - 18 =

We'll write out the equation:
\[
4(s - 3) - 18 = 0
\]

1. Distribute the \(4\):
\[
4s - 12 - 18 = 0
\]
Simplifying gives:
\[
4s - 30 = 0
\]

2. Now, add \(30\) to both sides:
\[
4s = 30
\]

3. Divide by \(4\):
\[
s = \frac{30}{4} = 7.5
\]

So, the value of \(s\) that is a solution is:
\[
s = 7.5
\]

---

### 4. Identify the property of equality shown
The property of equality used here is the **Addition Property of Equality**. It states that if two expressions are equal, you can add (or subtract) the same value to both sides of the equation without changing the equality.

In this case:
If \(-40 - t = s\), then adding \(-79\) to both sides gives:
\[
-79 - 40 - t = -79 + s
\]

So, the property used is the **Addition Property of Equality**.