(multiplication & division)
directions: solve each equation. show your work and check your solution
1. ( 4x = 28 )
2. ( \frac{a}{-2} = 6 )
3. ( -64 = 3 - a )
4. ( -3 = \frac{2}{4} ) (note: this might be a typo, likely ( -3 = \frac{z}{4} ) or similar)
5. ( -n = 4 )
6. ( -7k = -84 )
7. ( \frac{y}{-6} = 3 )
8. ( -17r = 51 )
9. ( -9 = \frac{h}{-5} )
10. ( 0 = 9n )
11. ( \frac{m}{-3} = 16 )
12. ( 5v = 65 )
directions: translate and solve each equation. show your work and check your solution.
13. he quotient of a number and 3 is 8.\
14.
ine times a number is -63.\
15. wice a number is 26.\
16. he product of a number and -8 is 72.\

Question

(multiplication & division)
directions: solve each equation. show your work and check your solution
1. ( 4x = 28 )
2. ( \frac{a}{-2} = 6 )
3. ( -64 = 3 - a )
4. ( -3 = \frac{2}{4} ) (note: this might be a typo, likely ( -3 = \frac{z}{4} ) or similar)
5. ( -n = 4 )
6. ( -7k = -84 )
7. ( \frac{y}{-6} = 3 )
8. ( -17r = 51 )
9. ( -9 = \frac{h}{-5} )
10. ( 0 = 9n )
11. ( \frac{m}{-3} = 16 )
12. ( 5v = 65 )
directions: translate and solve each equation. show your work and check your solution.
13. 	he quotient of a number and 3 is 8.\
14.
ine times a number is -63.\
15. 	wice a number is 26.\
16. 	he product of a number and -8 is 72.\

Accepted Answer

### Problem 1: $ 4x = 28 $
# Explanation:
## Step 1: Isolate $ x $ by dividing both sides by 4.
To solve for $ x $, we use the inverse operation of multiplication, which is division. We divide both sides of the equation $ 4x = 28 $ by 4.
$$
\frac{4x}{4} = \frac{28}{4}
$$
## Step 2: Simplify both sides.
Simplifying the left side, $ \frac{4x}{4} = x $. Simplifying the right side, $ \frac{28}{4} = 7 $. So we get $ x = 7 $.
## Step 3: Check the solution.
Substitute $ x = 7 $ back into the original equation: $ 4(7) = 28 $, which simplifies to $ 28 = 28 $. This is a true statement, so the solution is correct.
# Answer: $ x = 7 $

### Problem 2: $ \frac{a}{-2} = 6 $
# Explanation:
## Step 1: Isolate $ a $ by multiplying both sides by -2.
To solve for $ a $, we use the inverse operation of division, which is multiplication. We multiply both sides of the equation $ \frac{a}{-2} = 6 $ by -2.
$$
-2 \times \frac{a}{-2} = 6 \times -2
$$
## Step 2: Simplify both sides.
Simplifying the left side, $ -2 \times \frac{a}{-2} = a $. Simplifying the right side, $ 6 \times -2 = -12 $. So we get $ a = -12 $.
## Step 3: Check the solution.
Substitute $ a = -12 $ back into the original equation: $ \frac{-12}{-2} = 6 $, which simplifies to $ 6 = 6 $. This is a true statement, so the solution is correct.
# Answer: $ a = -12 $

### Problem 3: $ -64 = 3a $ (assuming it's $ -64 = 3a $, maybe a typo, should be $ -64 = 3a $ or $ -64 = 8a $? Wait, original is $ -64 = 3a $? Wait, maybe it's $ -64 = 8a $? Wait, the image shows "3 -a"? Wait, maybe it's $ -64 = 8a $? Wait, maybe the original is $ -64 = 8a $? Let's assume it's $ -64 = 8a $ (maybe a typo, 8a instead of 3 -a). Let's correct: If it's $ -64 = 8a $:
# Explanation:
## Step 1: Isolate $ a $ by dividing both sides by 8.
$$
\frac{-64}{8} = \frac{8a}{8}
$$
## Step 2: Simplify.
Left side: $ -8 $, right side: $ a $. So $ a = -8 $.
## Step 3: Check.
Substitute $ a = -8 $ into $ 8a $: $ 8(-8) = -64 $, which matches the left side. So $ a = -8 $.
(If the original is $ -64 = 3 - a $, then:
## Step 1: Subtract 3 from both sides.
$ -64 - 3 = -a $ → $ -67 = -a $
## Step 2: Multiply both sides by -1.
$ a = 67 $
But since the problem is about multiplication and division, likely $ -64 = 8a $, so we'll go with $ a = -8 $ assuming a typo.
# Answer: $ a = -8 $ (assuming $ -64 = 8a $)

### Problem 4: $ -3 = \frac{z}{4} $
# Explanation:
## Step 1: Isolate $ z $ by multiplying both sides by 4.
$$
-3 \times 4 = \frac{z}{4} \times 4
$$
## Step 2: Simplify.
Left side: $ -12 $, right side: $ z $. So $ z = -12 $.
## Step 3: Check.
Substitute $ z = -12 $ into $ \frac{z}{4} $: $ \frac{-12}{4} = -3 $, which matches the left side. Correct.
# Answer: $ z = -12 $

### Problem 5: $ -n = 4 $
# Explanation:
## Step 1: Isolate $ n $ by multiplying both sides by -1.
$$
(-1) \times (-n) = 4 \times (-1)
$$
## Step 2: Simplify.
Left side: $ n $, right side: $ -4 $. So $ n = -4 $.
## Step 3: Check.
Substitute $ n = -4 $ into $ -n $: $ -(-4) = 4 $, which matches the right side. Correct.
# Answer: $ n = -4 $

### Problem 6: $ -7k = -84 $
# Explanation:
## Step 1: Isolate $ k $ by dividing both sides by -7.
$$
\frac{-7k}{-7} = \frac{-84}{-7}
$$
## Step 2: Simplify.
Left side: $ k $, right side: $ 12 $. So $ k = 12 $.
## Step 3: Check.
Substitute $ k = 12 $ into $ -7k $: $ -7(12) = -84 $, which matches the right side. Correct.
# Answer: $ k = 12 $

### Problem 7: $ \frac{y}{-6} = 3 $
# Explanation:
## Step 1: Isolate $ y $ by multiplying both sides by -6.
$$
\frac{y}{-6} \times (-6) = 3 \times (-6)
$$
## Step 2: Simplify.
Left side: $ y $, right side: $ -18 $. So $ y = -18 $.
## Step 3: Check.
Substitute $ y = -18 $ into $ \frac{y}{-6} $: $ \frac{-18}{-6} = 3 $, which matches the right side. Correct.
# Answer: $ y = -18 $

### Problem 8: $ -17r = 51 $
# Explanation:
## Step 1: Isolate $ r $ by dividing both sides by -17.
$$
\frac{-17r}{-17} = \frac{51}{-17}
$$
## Step 2: Simplify.
Left side: $ r $, right side: $ -3 $. So $ r = -3 $.
## Step 3: Check.
Substitute $ r = -3 $ into $ -17r $: $ -17(-3) = 51 $, which matches the right side. Correct.
# Answer: $ r = -3 $

### Problem 9: $ -9 = \frac{h}{-5} $
# Explanation:
## Step 1: Isolate $ h $ by multiplying both sides by -5.
$$
-9 \times (-5) = \frac{h}{-5} \times (-5)
$$
## Step 2: Simplify.
Left side: $ 45 $, right side: $ h $. So $ h = 45 $.
## Step 3: Check.
Substitute $ h = 45 $ into $ \frac{h}{-5} $: $ \frac{45}{-5} = -9 $, which matches the left side. Correct.
# Answer: $ h = 45 $

### Problem 10: $ 0 = 9n $
# Explanation:
## Step 1: Isolate $ n $ by dividing both sides by 9.
$$
\frac{0}{9} = \frac{9n}{9}
$$
## Step 2: Simplify.
Left side: $ 0 $, right side: $ n $. So $ n = 0 $.
## Step 3: Check.
Substitute $ n = 0 $ into $ 9n $: $ 9(0) = 0 $, which matches the left side. Correct.
# Answer: $ n = 0 $

### Problem 11: $ \frac{m}{-3} = 16 $
# Explanation:
## Step 1: Isolate $ m $ by multiplying both sides by -3.
$$
\frac{m}{-3} \times (-3) = 16 \times (-3)
$$
## Step 2: Simplify.
Left side: $ m $, right side: $ -48 $. So $ m = -48 $.
## Step 3: Check.
Substitute $ m = -48 $ into $ \frac{m}{-3} $: $ \frac{-48}{-3} = 16 $, which matches the right side. Correct.
# Answer: $ m = -48 $

### Problem 12: $ 5v = 65 $
# Explanation:
## Step 1: Isolate $ v $ by dividing both sides by 5.
$$
\frac{5v}{5} = \frac{65}{5}
$$
## Step 2: Simplify.
Left side: $ v $, right side: $ 13 $. So $ v = 13 $.
## Step 3: Check.
Substitute $ v = 13 $ into $ 5v $: $ 5(13) = 65 $, which matches the right side. Correct.
# Answer: $ v = 13 $

### Problem 13: "The quotient of a number and 3 is 8."
# Explanation:
## Step 1: Translate the sentence into an equation.
Let the number be $ x $. The quotient of $ x $ and 3 is $ \frac{x}{3} $, and this equals 8. So the equation is $ \frac{x}{3} = 8 $.
## Step 2: Solve for $ x $ by multiplying both sides by 3.
$$
x = 8 \times 3
$$
## Step 3: Simplify.
$ x = 24 $.
## Step 4: Check.
The quotient of 24 and 3 is $ \frac{24}{3} = 8 $, which matches the problem statement. Correct.
# Answer: The number is $ 24 $ (equation: $ \frac{x}{3} = 8 $, solution $ x = 24 $)

### Problem 14: "Nine times a number is -63."
# Explanation:
## Step 1: Translate the sentence into an equation.
Let the number be $ x $. Nine times $ x $ is $ 9x $, and this equals -63. So the equation is $ 9x = -63 $.
## Step 2: Solve for $ x $ by dividing both sides by 9.
$$
x = \frac{-63}{9}
$$
## Step 3: Simplify.
$ x = -7 $.
## Step 4: Check.
Nine times -7 is $ 9(-7) = -63 $, which matches the problem statement. Correct.
# Answer: The number is $ -7 $ (equation: $ 9x = -63 $, solution $ x = -7 $)

### Problem 15: "Twice a number is 26."
# Explanation:
## Step 1: Translate the sentence into an equation.
Let the number be $ x $. Twice $ x $ is $ 2x $, and this equals 26. So the equation is $ 2x = 26 $.
## Step 2: Solve for $ x $ by dividing both sides by 2.
$$
x = \frac{26}{2}
$$
## Step 3: Simplify.
$ x = 13 $.
## Step 4: Check.
Twice 13 is $ 2(13) = 26 $, which matches the problem statement. Correct.
# Answer: The number is $ 13 $ (equation: $ 2x = 26 $, solution $ x = 13 $)

### Problem 16: "The product of a number and -8 is 72."
# Explanation:
## Step 1: Translate the sentence into an equation.
Let the number be $ x $. The product of $ x $ and -8 is $ -8x $, and this equals 72. So the equation is $ -8x = 72 $.
## Step 2: Solve for $ x $ by dividing both sides by -8.
$$
x = \frac{72}{-8}
$$
## Step 3: Simplify.
$ x = -9 $.
## Step 4: Check.
The product of -9 and -8 is $ (-9)(-8) = 72 $, which matches the problem statement. Correct.
# Answer: The number is $ -9 $ (equation: $ -8x = 72 $, solution $ x = -9 $)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \( 4x = 28 \)

Step 1: Isolate \( x \) by dividing both sides by 4.

Step 2: Simplify both sides.

Step 3: Check the solution.

Step 1: Isolate \( a \) by multiplying both sides by -2.

Step 2: Simplify both sides.

Step 3: Check the solution.

Step 1: Isolate \( a \) by dividing both sides by 8.

Step 2: Simplify.

Step 3: Check.

Step 1: Subtract 3 from both sides.

Step 2: Multiply both sides by -1.

Answer:

Problem 2: \( \frac{a}{-2} = 6 \)