Question
\( \begin{array}{ll}\text { 3. } & 4 a+1=-11 \\ \text { 4. } & 6 b-3=9 \\ \text { 5. } & 5 c+8=3\end{array} \)
Ask by Klein Ross. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are:
- \( a = -3 \)
- \( b = 2 \)
- \( c = -1 \)
Solution
Certainly! Let's solve each of the equations step by step.
---
### **3. \( 4a + 1 = -11 \)**
**Step 1:** Subtract 1 from both sides to isolate the term with \( a \).
\[
4a + 1 - 1 = -11 - 1
\]
\[
4a = -12
\]
**Step 2:** Divide both sides by 4 to solve for \( a \).
\[
\frac{4a}{4} = \frac{-12}{4}
\]
\[
a = -3
\]
---
### **4. \( 6b - 3 = 9 \)**
**Step 1:** Add 3 to both sides to isolate the term with \( b \).
\[
6b - 3 + 3 = 9 + 3
\]
\[
6b = 12
\]
**Step 2:** Divide both sides by 6 to solve for \( b \).
\[
\frac{6b}{6} = \frac{12}{6}
\]
\[
b = 2
\]
---
### **5. \( 5c + 8 = 3 \)**
**Step 1:** Subtract 8 from both sides to isolate the term with \( c \).
\[
5c + 8 - 8 = 3 - 8
\]
\[
5c = -5
\]
**Step 2:** Divide both sides by 5 to solve for \( c \).
\[
\frac{5c}{5} = \frac{-5}{5}
\]
\[
c = -1
\]
---
### **Summary of Solutions**
- \( a = -3 \)
- \( b = 2 \)
- \( c = -1 \)
If you have any further questions or need additional assistance, feel free to ask!
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Bonus Knowledge
To solve these equations, you'll want to isolate the variable on one side. For example, in the first equation, \(4a + 1 = -11\), subtract 1 from both sides to get \(4a = -12\). Then, divide both sides by 4 to find \(a = -3\). Moving on to the second equation \(6b - 3 = 9\), add 3 to both sides to have \(6b = 12\). Divide by 6 to discover that \(b = 2\). Finally, for the third equation \(5c + 8 = 3\), subtract 8 from both sides to get \(5c = -5\), and then divide by 5 to find \(c = -1\). Now we have: 1. \(a = -3\) 2. \(b = 2\) 3. \(c = -1\)