1. $$ 3(x+2)=18 $$ 2. $$ 2(3 y-1)=16 $$ 3. $$ 4 a+3-a=12 $$ 4. $$ 5 b-2+2 b=19 $$ 5. $$ -2(c+4)=6 $$

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UpStudy AI · Accepted Answer

Let's solve each of the given equations step by step.

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**1. $$ 3(x + 2) = 18 $$**

**Solution:**
$$
\begin{align*}
3(x + 2) &= 18 \
x + 2 &= \frac{18}{3} \quad \text{(Divide both sides by 3)} \
x + 2 &= 6 \
x &= 6 - 2 \
x &= 4
\end{align*}
$$

**Answer:** $$ x = 4 $$

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**2. $$ 2(3y - 1) = 16 $$**

**Solution:**
$$
\begin{align*}
2(3y - 1) &= 16 \
3y - 1 &= \frac{16}{2} \quad \text{(Divide both sides by 2)} \
3y - 1 &= 8 \
3y &= 8 + 1 \
3y &= 9 \
y &= \frac{9}{3} \
y &= 3
\end{align*}
$$

**Answer:** $$ y = 3 $$

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**3. $$ 4a + 3 - a = 12 $$**

**Solution:**
$$
\begin{align*}
4a + 3 - a &= 12 \
(4a - a) + 3 &= 12 \
3a + 3 &= 12 \
3a &= 12 - 3 \
3a &= 9 \
a &= \frac{9}{3} \
a &= 3
\end{align*}
$$

**Answer:** $$ a = 3 $$

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**4. $$ 5b - 2 + 2b = 19 $$**

**Solution:**
$$
\begin{align*}
5b - 2 + 2b &= 19 \
(5b + 2b) - 2 &= 19 \
7b - 2 &= 19 \
7b &= 19 + 2 \
7b &= 21 \
b &= \frac{21}{7} \
b &= 3
\end{align*}
$$

**Answer:** $$ b = 3 $$

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**5. $$ -2(c + 4) = 6 $$**

**Solution:**
$$
\begin{align*}
-2(c + 4) &= 6 \
c + 4 &= \frac{6}{-2} \quad \text{(Divide both sides by -2)} \
c + 4 &= -3 \
c &= -3 - 4 \
c &= -7
\end{align*}
$$

**Answer:** $$ c = -7 $$

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Feel free to reach out if you have any more questions!
Here are the solutions to the equations: 1. $$ x = 4 $$ 2. $$ y = 3 $$ 3. $$ a = 3 $$ 4. $$ b = 3 $$ 5. $$ c = -7 $$

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