Question

1. $30 = 10a$
2. $21 = 3a$
3. $-45 = 9k$
4. $-90 = 10x$
5. $4 = -4p$
6. $56 = -7n$
7. $-32 = -8x$
8. $-80 = -10n$
9. $10 = \frac{x}{8}$
10. $3 = \frac{m}{6}$
11. $-8 = \frac{n}{10}$
12. $-9 = \frac{x}{3}$
13. $9 = \frac{r}{-2}$
14. $7 = \frac{k}{-3}$
15. $-9 = \frac{m}{-8}$
16. $-1 = \frac{k}{-10}$
17. $0 = -7b$
18. $3 = \frac{m}{4}$

Explanation:

Let's solve these linear equations one by one. We'll use the multiplication or division property of equality to isolate the variable.

Problem 19: \( 30 = 10a \)

Step 1: Isolate \( a \)

Divide both sides by 10:
\( \frac{30}{10} = \frac{10a}{10} \)
\( 3 = a \) or \( a = 3 \)

Problem 20: \( 21 = 3a \)

Step 1: Isolate \( a \)

Divide both sides by 3:
\( \frac{21}{3} = \frac{3a}{3} \)
\( 7 = a \) or \( a = 7 \)

Problem 21: \( -45 = 9k \)

Step 1: Isolate \( k \)

Divide both sides by 9:
\( \frac{-45}{9} = \frac{9k}{9} \)
\( -5 = k \) or \( k = -5 \)

Problem 22: \( -90 = 10x \)

Step 1: Isolate \( x \)

Divide both sides by 10:
\( \frac{-90}{10} = \frac{10x}{10} \)
\( -9 = x \) or \( x = -9 \)

Problem 23: \( 4 = -4p \)

Step 1: Isolate \( p \)

Divide both sides by -4:
\( \frac{4}{-4} = \frac{-4p}{-4} \)
\( -1 = p \) or \( p = -1 \)

Problem 24: \( 56 = -7n \)

Step 1: Isolate \( n \)

Divide both sides by -7:
\( \frac{56}{-7} = \frac{-7n}{-7} \)
\( -8 = n \) or \( n = -8 \)

Problem 25: \( -32 = -8x \)

Step 1: Isolate \( x \)

Divide both sides by -8:
\( \frac{-32}{-8} = \frac{-8x}{-8} \)
\( 4 = x \) or \( x = 4 \)

Problem 26: \( -80 = -10n \)

Step 1: Isolate \( n \)

Divide both sides by -10:
\( \frac{-80}{-10} = \frac{-10n}{-10} \)
\( 8 = n \) or \( n = 8 \)

Problem 27: \( 10 = \frac{x}{8} \)

Step 1: Isolate \( x \)

Multiply both sides by 8:
\( 10 \times 8 = \frac{x}{8} \times 8 \)
\( 80 = x \) or \( x = 80 \)

Problem 28: \( 3 = \frac{m}{6} \)

Step 1: Isolate \( m \)

Multiply both sides by 6:
\( 3 \times 6 = \frac{m}{6} \times 6 \)
\( 18 = m \) or \( m = 18 \)

Problem 29: \( -8 = \frac{n}{10} \)

Step 1: Isolate \( n \)

Multiply both sides by 10:
\( -8 \times 10 = \frac{n}{10} \times 10 \)
\( -80 = n \) or \( n = -80 \)

Problem 30: \( -9 = \frac{x}{3} \)

Step 1: Isolate \( x \)

Multiply both sides by 3:
\( -9 \times 3 = \frac{x}{3} \times 3 \)
\( -27 = x \) or \( x = -27 \)

Problem 31: \( 9 = \frac{r}{-2} \)

Step 1: Isolate \( r \)

Multiply both sides by -2:
\( 9 \times (-2) = \frac{r}{-2} \times (-2) \)
\( -18 = r \) or \( r = -18 \)

Problem 32: \( 7 = \frac{k}{-3} \)

Step 1: Isolate \( k \)

Multiply both sides by -3:
\( 7 \times (-3) = \frac{k}{-3} \times (-3) \)
\( -21 = k \) or \( k = -21 \)

Problem 33: \( -9 = \frac{m}{-8} \)

Step 1: Isolate \( m \)

Multiply both sides by -8:
\( -9 \times (-8) = \frac{m}{-8} \times (-8) \)
\( 72 = m \) or \( m = 72 \)

Problem 34: \( -1 = \frac{k}{-10} \)

Step 1: Isolate \( k \)

Multiply both sides by -10:
\( -1 \times (-10) = \frac{k}{-10} \times (-10) \)
\( 10 = k \) or \( k = 10 \)

Problem 35: \( 0 = -7b \)

Step 1: Isolate \( b \)

Divide both sides by -7:
\( \frac{0}{-7} = \frac{-7b}{-7} \)
\( 0 = b \) or \( b = 0 \)

Problem 36: \( 3 = \frac{m}{4} \)

Step 1: Isolate \( m \)

Multiply both sides by 4:
\( 3 \times 4 = \frac{m}{4} \times 4 \)
\( 12 = m \) or \( m = 12 \)

Summary of Answers:

1. \( a = 3 \)
2. \( a = 7 \)
3. \( k = -5 \)
4. \( x = -9 \)
5. \( p = -1 \)
6. \( n = -8 \)
7. \( x = 4 \)
8. \( n = 8 \)
9. \( x = 80 \)
10. \( m = 18 \)
11. \( n = -80 \)
12. \( x = -27 \)
13. \( r = -18 \)
14. \( k = -21 \)
15. \( m = 72 \)
16. \( k = 10 \)
17. \( b = 0 \)
18. \( m = 12 \)

Answer:

Let's solve these linear equations one by one. We'll use the multiplication or division property of equality to isolate the variable.

Problem 19: \( 30 = 10a \)

Step 1: Isolate \( a \)

Divide both sides by 10:
\( \frac{30}{10} = \frac{10a}{10} \)
\( 3 = a \) or \( a = 3 \)

Problem 20: \( 21 = 3a \)

Step 1: Isolate \( a \)

Divide both sides by 3:
\( \frac{21}{3} = \frac{3a}{3} \)
\( 7 = a \) or \( a = 7 \)

Problem 21: \( -45 = 9k \)

Step 1: Isolate \( k \)

Divide both sides by 9:
\( \frac{-45}{9} = \frac{9k}{9} \)
\( -5 = k \) or \( k = -5 \)

Problem 22: \( -90 = 10x \)

Step 1: Isolate \( x \)

Divide both sides by 10:
\( \frac{-90}{10} = \frac{10x}{10} \)
\( -9 = x \) or \( x = -9 \)

Problem 23: \( 4 = -4p \)

Step 1: Isolate \( p \)

Divide both sides by -4:
\( \frac{4}{-4} = \frac{-4p}{-4} \)
\( -1 = p \) or \( p = -1 \)

Problem 24: \( 56 = -7n \)

Step 1: Isolate \( n \)

Divide both sides by -7:
\( \frac{56}{-7} = \frac{-7n}{-7} \)
\( -8 = n \) or \( n = -8 \)

Problem 25: \( -32 = -8x \)

Step 1: Isolate \( x \)

Divide both sides by -8:
\( \frac{-32}{-8} = \frac{-8x}{-8} \)
\( 4 = x \) or \( x = 4 \)

Problem 26: \( -80 = -10n \)

Step 1: Isolate \( n \)

Divide both sides by -10:
\( \frac{-80}{-10} = \frac{-10n}{-10} \)
\( 8 = n \) or \( n = 8 \)

Problem 27: \( 10 = \frac{x}{8} \)

Step 1: Isolate \( x \)

Multiply both sides by 8:
\( 10 \times 8 = \frac{x}{8} \times 8 \)
\( 80 = x \) or \( x = 80 \)

Problem 28: \( 3 = \frac{m}{6} \)

Step 1: Isolate \( m \)

Multiply both sides by 6:
\( 3 \times 6 = \frac{m}{6} \times 6 \)
\( 18 = m \) or \( m = 18 \)

Problem 29: \( -8 = \frac{n}{10} \)

Step 1: Isolate \( n \)

Multiply both sides by 10:
\( -8 \times 10 = \frac{n}{10} \times 10 \)
\( -80 = n \) or \( n = -80 \)

Problem 30: \( -9 = \frac{x}{3} \)

Step 1: Isolate \( x \)

Multiply both sides by 3:
\( -9 \times 3 = \frac{x}{3} \times 3 \)
\( -27 = x \) or \( x = -27 \)

Problem 31: \( 9 = \frac{r}{-2} \)

Step 1: Isolate \( r \)

Multiply both sides by -2:
\( 9 \times (-2) = \frac{r}{-2} \times (-2) \)
\( -18 = r \) or \( r = -18 \)

Problem 32: \( 7 = \frac{k}{-3} \)

Step 1: Isolate \( k \)

Multiply both sides by -3:
\( 7 \times (-3) = \frac{k}{-3} \times (-3) \)
\( -21 = k \) or \( k = -21 \)

Problem 33: \( -9 = \frac{m}{-8} \)

Step 1: Isolate \( m \)

Multiply both sides by -8:
\( -9 \times (-8) = \frac{m}{-8} \times (-8) \)
\( 72 = m \) or \( m = 72 \)

Problem 34: \( -1 = \frac{k}{-10} \)

Step 1: Isolate \( k \)

Multiply both sides by -10:
\( -1 \times (-10) = \frac{k}{-10} \times (-10) \)
\( 10 = k \) or \( k = 10 \)

Problem 35: \( 0 = -7b \)

Step 1: Isolate \( b \)

Divide both sides by -7:
\( \frac{0}{-7} = \frac{-7b}{-7} \)
\( 0 = b \) or \( b = 0 \)

Problem 36: \( 3 = \frac{m}{4} \)

Step 1: Isolate \( m \)

Multiply both sides by 4:
\( 3 \times 4 = \frac{m}{4} \times 4 \)
\( 12 = m \) or \( m = 12 \)

Summary of Answers:

1. \( a = 3 \)
2. \( a = 7 \)
3. \( k = -5 \)
4. \( x = -9 \)
5. \( p = -1 \)
6. \( n = -8 \)
7. \( x = 4 \)
8. \( n = 8 \)
9. \( x = 80 \)
10. \( m = 18 \)
11. \( n = -80 \)
12. \( x = -27 \)
13. \( r = -18 \)
14. \( k = -21 \)
15. \( m = 72 \)
16. \( k = 10 \)
17. \( b = 0 \)
18. \( m = 12 \)