The problem asks us to solve a series of linear equations for the unknown variables. The equations are: 1. $3a - 7 = 26$

1. Problem Description

The problem asks us to solve a series of linear equations for the unknown variables. The equations are:

1. $3a - 7 = 26$

2. $9f + 5 = 77$

3. $2k - 20 = 40$

4. $6b - 4 = 38$

5. $10h + 58 = -2$

6. $-4d + 17 = 65$

7. $8m + 11 = -53$

8. $5z - 1.75 = 8.25$

9. $\frac{1}{2}n + 40 = 55$

1

0. $-\frac{1}{4}c - 5 = 20$

1

1. $4.8g + 9 = 33$

1

2. $\frac{1}{3}p + 22 = 18$

1

3. $1.2y + 0.52 = 7$

1

4. $2.5t + 24 = 14$

1

5. $5j + \frac{2}{3} = -\frac{1}{6}$

2. Solution Steps

1. $3a - 7 = 26$

Add 7 to both sides: $3a = 33$

Divide by 3: $a = 11$

2. $9f + 5 = 77$

Subtract 5 from both sides: $9f = 72$

Divide by 9: $f = 8$

3. $2k - 20 = 40$

Add 20 to both sides: $2k = 60$

Divide by 2: $k = 30$

4. $6b - 4 = 38$

Add 4 to both sides: $6b = 42$

Divide by 6: $b = 7$

5. $10h + 58 = -2$

Subtract 58 from both sides: $10h = -60$

Divide by 10: $h = -6$

6. $-4d + 17 = 65$

Subtract 17 from both sides: $-4d = 48$

Divide by -4: $d = -12$

7. $8m + 11 = -53$

Subtract 11 from both sides: $8m = -64$

Divide by 8: $m = -8$

8. $5z - 1.75 = 8.25$

Add 1.75 to both sides: $5z = 10$

Divide by 5: $z = 2$

9. $\frac{1}{2}n + 40 = 55$

Subtract 40 from both sides: $\frac{1}{2}n = 15$

Multiply by 2: $n = 30$

1

0. $-\frac{1}{4}c - 5 = 20$

Add 5 to both sides: $-\frac{1}{4}c = 25$

Multiply by -4: $c = -100$

1

1. $4.8g + 9 = 33$

Subtract 9 from both sides: $4.8g = 24$

Divide by 4.8: $g = 5$

1

2. $\frac{1}{3}p + 22 = 18$

Subtract 22 from both sides: $\frac{1}{3}p = -4$

Multiply by 3: $p = -12$

1

3. $1.2y + 0.52 = 7$

Subtract 0.52 from both sides: $1.2y = 6.48$

Divide by 1.2: $y = 5.4$

1

4. $2.5t + 24 = 14$

Subtract 24 from both sides: $2.5t = -10$

Divide by 2.5: $t = -4$

1

5. $5j + \frac{2}{3} = -\frac{1}{6}$

Subtract $\frac{2}{3}$ from both sides: $5j = -\frac{1}{6} - \frac{2}{3} = -\frac{1}{6} - \frac{4}{6} = -\frac{5}{6}$

Divide by 5: $j = -\frac{5}{6} \cdot \frac{1}{5} = -\frac{1}{6}$

3. Final Answer

1. $a = 11$

2. $f = 8$

3. $k = 30$

4. $b = 7$

5. $h = -6$

6. $d = -12$

7. $m = -8$

8. $z = 2$

9. $n = 30$

1

0. $c = -100$

1

1. $g = 5$

1

2. $p = -12$

1

3. $y = 5.4$

1

4. $t = -4$

1

5. $j = -\frac{1}{6}$