Question

equation 312 = 52n inverse operation solution check equation 4.5 + n = 13.2 inverse operation solution check equation n/6 = 3 inverse operation solution check last friday trevon had $29. over the weekend he received some money for cleaning the attic. he now has $41. how much money did he receive? select all of the equations equivalent to 6z = 42. a z - 7 = 0 b (4x)/2 = 14 c x - 1 = 8 d 6x - 1 = 23 storytime which equation best represents the situation? if you get stuck, consider drawing a diagram. x + 5 = 20 x = 20 + 5 5x = 20 x + 20 = 5 5 + 20 = x (1/20) = x after elena ran 5 miles on friday, she had run a total of 20 miles for the week. she ran x miles before friday. prove that the solution x = 15 makes the equation true.

Explanation:

First Equation: \( 312 = 52n \)

Step1: Inverse Operation (Division)

To isolate \( n \), we use the inverse operation of multiplication, which is division. We divide both sides of the equation by 52.
\( \frac{312}{52} = \frac{52n}{52} \)

Step2: Solution

Simplify the equation:
\( n = \frac{312}{52} = 6 \)

Step3: Check

Substitute \( n = 6 \) back into the original equation:
Left side: \( 312 \)
Right side: \( 52 \times 6 = 312 \)
Since \( 312 = 312 \), the solution is correct.

Second Equation: \( 4.5 + n = 13.2 \)

Step1: Inverse Operation (Subtraction)

To isolate \( n \), we use the inverse operation of addition, which is subtraction. We subtract 4.5 from both sides.
\( 4.5 + n - 4.5 = 13.2 - 4.5 \)

Step2: Solution

Simplify the equation:
\( n = 13.2 - 4.5 = 8.7 \)

Step3: Check

Substitute \( n = 8.7 \) back into the original equation:
Left side: \( 4.5 + 8.7 = 13.2 \)
Right side: \( 13.2 \)
Since \( 13.2 = 13.2 \), the solution is correct.

Third Equation: \( \frac{n}{6} = 3 \)

Step1: Inverse Operation (Multiplication)

To isolate \( n \), we use the inverse operation of division, which is multiplication. We multiply both sides by 6.
\( \frac{n}{6} \times 6 = 3 \times 6 \)

Step2: Solution

Simplify the equation:
\( n = 18 \)

Step3: Check

Substitute \( n = 18 \) back into the original equation:
Left side: \( \frac{18}{6} = 3 \)
Right side: \( 3 \)
Since \( 3 = 3 \), the solution is correct.

Money Problem:

Answer:

s:

• For \( 312 = 52n \):

Inverse Operation: Division
Solution: \( n = 6 \)
Check: \( 52 \times 6 = 312 \)

• For \( 4.5 + n = 13.2 \):

Inverse Operation: Subtraction
Solution: \( n = 8.7 \)
Check: \( 4.5 + 8.7 = 13.2 \)

• For \( \frac{n}{6} = 3 \):

Inverse Operation: Multiplication
Solution: \( n = 18 \)
Check: \( \frac{18}{6} = 3 \)

• Money Problem: Trevon received \$12.

• Equivalent Equations: A. \( z - 7 = 0 \), B. \( \frac{4z}{2} = 14 \)