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Consider the following equation.

2/3x−5=27


Determine the best TWO steps to solve the equation.

Identify the solution.

(3 points)

Step 1:
Step 2:
solution:
Multiply both sides of the equation by (2)/(3).
Subtract 5 from both sides of the equation.
Add 5 to both sides of the equation.
:: Divide both sides of the equation by (2)/(3).
Divide both sides of the equation by (3)/(2).
:: x=14(2)/(3)
x=18
x=48

9 answers

To solve the equation \( \frac{2}{3}x - 5 = 27 \), we can proceed with the following steps:

Step 1: Add 5 to both sides of the equation.
This gives us: \[ \frac{2}{3}x - 5 + 5 = 27 + 5 \] \[ \frac{2}{3}x = 32 \]

Step 2: Multiply both sides of the equation by \( \frac{3}{2} \).
This gives us: \[ \frac{3}{2} \cdot \frac{2}{3}x = 32 \cdot \frac{3}{2} \] \[ x = 48 \]

Solution: \( x = 48 \)

Summary of Steps:

  • Step 1: Add 5 to both sides.
  • Step 2: Multiply both sides by \( \frac{3}{2} \).

The solution is \( x = 48 \).

Consider the equation.

−2x−5=−21


Determine the best TWO steps to solve the equation.

Identify the solution.

(3 points)
Step 1:
Step 2:
Step 3:
Subtract 5 from both sides of the equation.
Add 5 to both sides of the equation.
Add 2 to both sides of the equation.
Multiply both sides of the equation with -2.
Divide both sides of the equation with -2.
x=-8
x=13
x=-13
x=8

To solve the equation \( -2x - 5 = -21 \), we can proceed with the following steps:

Step 1: Add 5 to both sides of the equation.
This gives us: \[ -2x - 5 + 5 = -21 + 5 \] \[ -2x = -16 \]

Step 2: Divide both sides of the equation by -2.
This gives us: \[ \frac{-2x}{-2} = \frac{-16}{-2} \] \[ x = 8 \]

Solution: \( x = 8 \)

Summary of Steps:

  • Step 1: Add 5 to both sides.
  • Step 2: Divide both sides by -2.

The solution is \( x = 8 \).

Determine the solution to the following problem:

n/5+10=−20


(1 point)
Responses

-150
-150

-50
-50

-6
-6

-2

To solve the equation \( \frac{n}{5} + 10 = -20 \), we can follow these steps:

  1. Subtract 10 from both sides of the equation: \[ \frac{n}{5} + 10 - 10 = -20 - 10 \] \[ \frac{n}{5} = -30 \]

  2. Multiply both sides by 5 to isolate \( n \): \[ n = -30 \times 5 \] \[ n = -150 \]

Therefore, the solution is:

Response: -150

Destiny opens a checking account with $100 and then deposits $27 each week. How many weeks will it take her account to reach $343?

Use the following equation to solve the problem: 100 + 27w = 343

(1 point)
Responses

16.4 weeks
16.4 weeks

12.7 weeks
12.7 weeks

9 weeks
9 weeks

3.16 weeks

To solve the equation \( 100 + 27w = 343 \), where \( w \) represents the number of weeks, we can follow these steps:

  1. Subtract 100 from both sides to isolate the term with \( w \): \[ 27w = 343 - 100 \] \[ 27w = 243 \]

  2. Divide both sides by 27 to find \( w \): \[ w = \frac{243}{27} \] \[ w = 9 \]

Thus, it will take Destiny 9 weeks for her account to reach $343.

Response: 9 weeks

Ahmadullah's basketball team will play 21 games this season. That is 12 more games than 1/3
the number of games they played last season. How many games did they play last season?

Use this equation to solve this problem: 1/3
g + 12 = 21

(1 point)
Responses

27 games
27 games

33 games
33 games

7 games
7 games

11 games

To solve the equation \( \frac{1}{3}g + 12 = 21 \), where \( g \) represents the number of games Ahmadullah's basketball team played last season, we can follow these steps:

  1. Subtract 12 from both sides: \[ \frac{1}{3}g = 21 - 12 \] \[ \frac{1}{3}g = 9 \]

  2. Multiply both sides by 3 to solve for \( g \): \[ g = 9 \times 3 \] \[ g = 27 \]

Thus, the number of games they played last season is 27 games.

Response: 27 games