We need to solve the following equations for $x$: 11. $5x - 3(x-1) = 39$ 12. $3x + 2(x-5) = 15$ 13. $7 - (x+1) = 9 - (2x-1)$ 14. $10x - (2x+3) = 21$ 15. $5(1-2x) - 3(4+4x) = 0$

AlgebraLinear EquationsSolving Equations
2025/6/23

1. Problem Description

We need to solve the following equations for xx:
1

1. $5x - 3(x-1) = 39$

1

2. $3x + 2(x-5) = 15$

1

3. $7 - (x+1) = 9 - (2x-1)$

1

4. $10x - (2x+3) = 21$

1

5. $5(1-2x) - 3(4+4x) = 0$

2. Solution Steps

1

1. $5x - 3(x-1) = 39$

Distribute the 3-3:
5x3x+3=395x - 3x + 3 = 39
Combine like terms:
2x+3=392x + 3 = 39
Subtract 3 from both sides:
2x=362x = 36
Divide both sides by 2:
x=18x = 18
1

2. $3x + 2(x-5) = 15$

Distribute the 2:
3x+2x10=153x + 2x - 10 = 15
Combine like terms:
5x10=155x - 10 = 15
Add 10 to both sides:
5x=255x = 25
Divide both sides by 5:
x=5x = 5
1

3. $7 - (x+1) = 9 - (2x-1)$

Distribute the 1-1:
7x1=92x+17 - x - 1 = 9 - 2x + 1
Combine like terms:
6x=102x6 - x = 10 - 2x
Add 2x2x to both sides:
6+x=106 + x = 10
Subtract 6 from both sides:
x=4x = 4
1

4. $10x - (2x+3) = 21$

Distribute the 1-1:
10x2x3=2110x - 2x - 3 = 21
Combine like terms:
8x3=218x - 3 = 21
Add 3 to both sides:
8x=248x = 24
Divide both sides by 8:
x=3x = 3
1

6. $5(1-2x) - 3(4+4x) = 0$

Distribute the 5 and -3:
510x1212x=05 - 10x - 12 - 12x = 0
Combine like terms:
22x7=0-22x - 7 = 0
Add 7 to both sides:
22x=7-22x = 7
Divide both sides by -22:
x=722x = -\frac{7}{22}

3. Final Answer

1

1. $x = 18$

1

2. $x = 5$

1

3. $x = 4$

1

4. $x = 3$

1

5. $x = -\frac{7}{22}$

Related problems in "Algebra"