Question
(1) \( 5 x+6=2 x+15 \) (2) \( 7 x-4=20+3 x \) (3) \( 2 x+15=43-5 x \) (4) \( 3+4 x=9 x+13 \) (5) \( 2 x-10=44+8 x \) (6) \( -7 x-2=24-9 x \) (7) \( 27-11 x=x-33 \) (B) \( 21 x+6=17 x-26 \) (9) \( 11 x=8 x-6 \) (10) \( -x-29=13+2 x \) (11) \( -18+5 x=-12 x-1 \) (12) \( -9 x-21=35-x \) (13) \( 7 x-2=-2 x-29 \) (14) \( 36+15 x=17 x \) (15) \( -15-4 x=6-3 x \) (16) \( 12 x-9=8 x-37 \) (17) \( -5 x+40=6 x-70 \) (18) \( -x-2=1-2 x \)
Ask by Chan Powell. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Here are the solutions to the equations:
1. \( x = 3 \)
2. \( x = 6 \)
3. \( x = 4 \)
4. \( x = -2 \)
5. \( x = -9 \)
6. \( x = 13 \)
7. \( x = 5 \)
8. \( x = -8 \)
9. \( x = -2 \)
10. \( x = -14 \)
11. \( x = 1 \)
12. \( x = -7 \)
13. \( x = -3 \)
14. \( x = 18 \)
15. \( x = -21 \)
16. \( x = -7 \)
17. \( x = 10 \)
18. \( x = 3 \)
Solution
Sure, let's solve each of the given linear equations step by step.
---
### **(1) \( 5x + 6 = 2x + 15 \)**
\[
\begin{align*}
5x + 6 &= 2x + 15 \\
5x - 2x &= 15 - 6 \\
3x &= 9 \\
x &= \frac{9}{3} \\
x &= 3
\end{align*}
\]
**Solution:** \( x = 3 \)
---
### **(2) \( 7x - 4 = 20 + 3x \)**
\[
\begin{align*}
7x - 3x &= 20 + 4 \\
4x &= 24 \\
x &= \frac{24}{4} \\
x &= 6
\end{align*}
\]
**Solution:** \( x = 6 \)
---
### **(3) \( 2x + 15 = 43 - 5x \)**
\[
\begin{align*}
2x + 5x &= 43 - 15 \\
7x &= 28 \\
x &= \frac{28}{7} \\
x &= 4
\end{align*}
\]
**Solution:** \( x = 4 \)
---
### **(4) \( 3 + 4x = 9x + 13 \)**
\[
\begin{align*}
3 - 13 &= 9x - 4x \\
-10 &= 5x \\
x &= \frac{-10}{5} \\
x &= -2
\end{align*}
\]
**Solution:** \( x = -2 \)
---
### **(5) \( 2x - 10 = 44 + 8x \)**
\[
\begin{align*}
2x - 8x &= 44 + 10 \\
-6x &= 54 \\
x &= \frac{54}{-6} \\
x &= -9
\end{align*}
\]
**Solution:** \( x = -9 \)
---
### **(6) \( -7x - 2 = 24 - 9x \)**
\[
\begin{align*}
-7x + 9x &= 24 + 2 \\
2x &= 26 \\
x &= \frac{26}{2} \\
x &= 13
\end{align*}
\]
**Solution:** \( x = 13 \)
---
### **(7) \( 27 - 11x = x - 33 \)**
\[
\begin{align*}
27 + 33 &= x + 11x \\
60 &= 12x \\
x &= \frac{60}{12} \\
x &= 5
\end{align*}
\]
**Solution:** \( x = 5 \)
---
### **(B) \( 21x + 6 = 17x - 26 \)**
\[
\begin{align*}
21x - 17x &= -26 - 6 \\
4x &= -32 \\
x &= \frac{-32}{4} \\
x &= -8
\end{align*}
\]
**Solution:** \( x = -8 \)
---
### **(9) \( 11x = 8x - 6 \)**
\[
\begin{align*}
11x - 8x &= -6 \\
3x &= -6 \\
x &= \frac{-6}{3} \\
x &= -2
\end{align*}
\]
**Solution:** \( x = -2 \)
---
### **(10) \( -x - 29 = 13 + 2x \)**
\[
\begin{align*}
-x - 2x &= 13 + 29 \\
-3x &= 42 \\
x &= \frac{42}{-3} \\
x &= -14
\end{align*}
\]
**Solution:** \( x = -14 \)
---
### **(11) \( -18 + 5x = -12x - 1 \)**
\[
\begin{align*}
5x + 12x &= -1 + 18 \\
17x &= 17 \\
x &= \frac{17}{17} \\
x &= 1
\end{align*}
\]
**Solution:** \( x = 1 \)
---
### **(12) \( -9x - 21 = 35 - x \)**
\[
\begin{align*}
-9x + x &= 35 + 21 \\
-8x &= 56 \\
x &= \frac{56}{-8} \\
x &= -7
\end{align*}
\]
**Solution:** \( x = -7 \)
---
### **(13) \( 7x - 2 = -2x - 29 \)**
\[
\begin{align*}
7x + 2x &= -29 + 2 \\
9x &= -27 \\
x &= \frac{-27}{9} \\
x &= -3
\end{align*}
\]
**Solution:** \( x = -3 \)
---
### **(14) \( 36 + 15x = 17x \)**
\[
\begin{align*}
36 &= 17x - 15x \\
36 &= 2x \\
x &= \frac{36}{2} \\
x &= 18
\end{align*}
\]
**Solution:** \( x = 18 \)
---
### **(15) \( -15 - 4x = 6 - 3x \)**
\[
\begin{align*}
-4x + 3x &= 6 + 15 \\
-x &= 21 \\
x &= -21
\end{align*}
\]
**Solution:** \( x = -21 \)
---
### **(16) \( 12x - 9 = 8x - 37 \)**
\[
\begin{align*}
12x - 8x &= -37 + 9 \\
4x &= -28 \\
x &= \frac{-28}{4} \\
x &= -7
\end{align*}
\]
**Solution:** \( x = -7 \)
---
### **(17) \( -5x + 40 = 6x - 70 \)**
\[
\begin{align*}
-5x - 6x &= -70 - 40 \\
-11x &= -110 \\
x &= \frac{-110}{-11} \\
x &= 10
\end{align*}
\]
**Solution:** \( x = 10 \)
---
### **(18) \( -x - 2 = 1 - 2x \)**
\[
\begin{align*}
-x + 2x &= 1 + 2 \\
x &= 3
\end{align*}
\]
**Solution:** \( x = 3 \)
---
### **Summary of Solutions:**
1. \( x = 3 \)
2. \( x = 6 \)
3. \( x = 4 \)
4. \( x = -2 \)
5. \( x = -9 \)
6. \( x = 13 \)
7. \( x = 5 \)
8. \( x = -8 \) *(Originally labeled as (B))*
9. \( x = -2 \)
10. \( x = -14 \)
11. \( x = 1 \)
12. \( x = -7 \)
13. \( x = -3 \)
14. \( x = 18 \)
15. \( x = -21 \)
16. \( x = -7 \)
17. \( x = 10 \)
18. \( x = 3 \)
---
Feel free to reach out if you have any further questions or need additional explanations!
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
To solve these equations, it can be helpful to remember some key algebraic strategies. One effective method is to isolate the variable on one side by performing the same operation on both sides of the equation. Always keep an eye out for opportunities to combine like terms, which simplifies your journey to the solution! Also, a common mistake when solving linear equations is forgetting to change the sign when moving a term from one side to the other. For instance, if you subtract \(2x\) from both sides, remember that it effectively changes its sign on the other side. Double-checking your signs can save you from unnecessary headaches later on!
