Question
determine the best TWO steps to solve the equation.
2/3x-5=27
Step 1:
Step 2:
Step 3:
options: 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=142/3, x=18,x=48
2/3x-5=27
Step 1:
Step 2:
Step 3:
options: 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=142/3, x=18,x=48
Answers
Answered by
GPT-4o mini
To solve the equation \( \frac{2}{3}x - 5 = 27 \), the best two steps would be:
**Step 1:** Add 5 to both sides of the equation.
This gives you:
\[
\frac{2}{3}x = 32
\]
**Step 2:** Multiply both sides of the equation by \( \frac{3}{2} \) (which is the same as dividing both sides by \( \frac{2}{3} \)).
This gives you:
\[
x = 32 \times \frac{3}{2} = 48
\]
So the best two steps are:
- **Add 5 to both sides of the equation**
- **Multiply both sides of the equation by \( \frac{3}{2} \) or divide both sides by \( \frac{2}{3} \)**
In summary, the correct steps are:
1. Add 5 to both sides of the equation.
2. Divide both sides of the equation by \( \frac{2}{3} \) or equivalently, multiply by \( \frac{3}{2} \).
**Step 1:** Add 5 to both sides of the equation.
This gives you:
\[
\frac{2}{3}x = 32
\]
**Step 2:** Multiply both sides of the equation by \( \frac{3}{2} \) (which is the same as dividing both sides by \( \frac{2}{3} \)).
This gives you:
\[
x = 32 \times \frac{3}{2} = 48
\]
So the best two steps are:
- **Add 5 to both sides of the equation**
- **Multiply both sides of the equation by \( \frac{3}{2} \) or divide both sides by \( \frac{2}{3} \)**
In summary, the correct steps are:
1. Add 5 to both sides of the equation.
2. Divide both sides of the equation by \( \frac{2}{3} \) or equivalently, multiply by \( \frac{3}{2} \).
Answer
can you tell me all 3 steps?
Answered by
GPT-4o mini
Sure! Here are all three steps to solve the equation \( \frac{2}{3}x - 5 = 27 \):
### Step 1:
**Add 5 to both sides of the equation.**
\[
\frac{2}{3}x - 5 + 5 = 27 + 5
\]
This simplifies to:
\[
\frac{2}{3}x = 32
\]
### Step 2:
**Multiply both sides of the equation by \( \frac{3}{2} \) (or equivalently, divide both sides by \( \frac{2}{3} \)).**
\[
x = 32 \times \frac{3}{2}
\]
This simplifies to:
\[
x = 48
\]
### Summary:
Putting it all together:
1. Add 5 to both sides to isolate the term with \( x \).
2. Multiply both sides by \( \frac{3}{2} \) to solve for \( x \).
3. The final solution is \( x = 48 \).
So the complete process is:
1. \( \frac{2}{3}x - 5 = 27 \) → \( \frac{2}{3}x = 32 \)
2. \( x = 32 \times \frac{3}{2} \) → \( x = 48 \)
### Step 1:
**Add 5 to both sides of the equation.**
\[
\frac{2}{3}x - 5 + 5 = 27 + 5
\]
This simplifies to:
\[
\frac{2}{3}x = 32
\]
### Step 2:
**Multiply both sides of the equation by \( \frac{3}{2} \) (or equivalently, divide both sides by \( \frac{2}{3} \)).**
\[
x = 32 \times \frac{3}{2}
\]
This simplifies to:
\[
x = 48
\]
### Summary:
Putting it all together:
1. Add 5 to both sides to isolate the term with \( x \).
2. Multiply both sides by \( \frac{3}{2} \) to solve for \( x \).
3. The final solution is \( x = 48 \).
So the complete process is:
1. \( \frac{2}{3}x - 5 = 27 \) → \( \frac{2}{3}x = 32 \)
2. \( x = 32 \times \frac{3}{2} \) → \( x = 48 \)
Answer
determine the best TWO steps to solve the equation.
-2x-5=-21
Step 1:
Step 2:
Step 3:
options: 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.
-2x-5=-21
Step 1:
Step 2:
Step 3:
options: 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.
Answered by
GPT-4o mini
To solve the equation \(-2x - 5 = -21\), the best two steps would be:
### Step 1:
**Add 5 to both sides of the equation.**
\[
-2x - 5 + 5 = -21 + 5
\]
This simplifies to:
\[
-2x = -16
\]
### Step 2:
**Divide both sides of the equation by -2.**
\[
x = \frac{-16}{-2}
\]
This simplifies to:
\[
x = 8
\]
### Summary:
So the complete steps are:
1. **Add 5 to both sides of the equation.**
2. **Divide both sides of the equation by -2.**
Thus, the best two steps are:
- **Add 5 to both sides of the equation**
- **Divide both sides of the equation by -2**
The final solution is \( x = 8 \).
### Step 1:
**Add 5 to both sides of the equation.**
\[
-2x - 5 + 5 = -21 + 5
\]
This simplifies to:
\[
-2x = -16
\]
### Step 2:
**Divide both sides of the equation by -2.**
\[
x = \frac{-16}{-2}
\]
This simplifies to:
\[
x = 8
\]
### Summary:
So the complete steps are:
1. **Add 5 to both sides of the equation.**
2. **Divide both sides of the equation by -2.**
Thus, the best two steps are:
- **Add 5 to both sides of the equation**
- **Divide both sides of the equation by -2**
The final solution is \( x = 8 \).
Answer
determine the solution to the following problem:
n/5+10=-20
a. -150
b. -50
c.-6
d.-2
n/5+10=-20
a. -150
b. -50
c.-6
d.-2
Answered by
GPT-4o mini
To solve the equation \( \frac{n}{5} + 10 = -20 \), follow these steps:
### Step 1:
**Subtract 10 from both sides of the equation.**
\[
\frac{n}{5} + 10 - 10 = -20 - 10
\]
This simplifies to:
\[
\frac{n}{5} = -30
\]
### Step 2:
**Multiply both sides by 5 to isolate \( n \).**
\[
n = -30 \times 5
\]
This simplifies to:
\[
n = -150
\]
### Conclusion:
The solution to the equation is \( n = -150 \).
Therefore, the correct answer is **a. -150**.
### Step 1:
**Subtract 10 from both sides of the equation.**
\[
\frac{n}{5} + 10 - 10 = -20 - 10
\]
This simplifies to:
\[
\frac{n}{5} = -30
\]
### Step 2:
**Multiply both sides by 5 to isolate \( n \).**
\[
n = -30 \times 5
\]
This simplifies to:
\[
n = -150
\]
### Conclusion:
The solution to the equation is \( n = -150 \).
Therefore, the correct answer is **a. -150**.
Answer
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+27=343
a. 16.4 weeks
b. 12.7 weeks
c. 9 weeks
d. 3.16 weeks
use the following equation to solve the problem: 100+27=343
a. 16.4 weeks
b. 12.7 weeks
c. 9 weeks
d. 3.16 weeks
Answered by
GPT-4o mini
To find out how many weeks it will take for Destiny's account to reach $343, we can set up the equation correctly.
The initial amount in the account is $100, and she deposits $27 each week. The amount in her account after \( w \) weeks can be expressed as:
\[
100 + 27w = 343
\]
### Step 1:
**Subtract $100 from both sides of the equation:**
\[
27w = 343 - 100
\]
\[
27w = 243
\]
### Step 2:
**Divide both sides by 27 to solve for \( w \):**
\[
w = \frac{243}{27}
\]
\[
w = 9
\]
### Conclusion:
It will take Destiny **9 weeks** to reach $343 in her checking account.
Therefore, the correct answer is **c. 9 weeks**.
The initial amount in the account is $100, and she deposits $27 each week. The amount in her account after \( w \) weeks can be expressed as:
\[
100 + 27w = 343
\]
### Step 1:
**Subtract $100 from both sides of the equation:**
\[
27w = 343 - 100
\]
\[
27w = 243
\]
### Step 2:
**Divide both sides by 27 to solve for \( w \):**
\[
w = \frac{243}{27}
\]
\[
w = 9
\]
### Conclusion:
It will take Destiny **9 weeks** to reach $343 in her checking account.
Therefore, the correct answer is **c. 9 weeks**.
Answer
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. how many games did they play last season?
use this equation to solve this problem: 1/3g +12=21
a. 27
b. 33
c. 7
d. 11
use this equation to solve this problem: 1/3g +12=21
a. 27
b. 33
c. 7
d. 11
Answered by
GPT-4o mini
To determine how many games Ahmadullah's team played last season, we can use the given equation:
\[
\frac{1}{3}g + 12 = 21
\]
where \( g \) is the number of games played last season.
### Step 1:
**Subtract 12 from both sides of the equation:**
\[
\frac{1}{3}g = 21 - 12
\]
\[
\frac{1}{3}g = 9
\]
### Step 2:
**Multiply both sides by 3 to solve for \( g \):**
\[
g = 9 \times 3
\]
\[
g = 27
\]
### Conclusion:
The team played **27 games** last season.
Therefore, the correct answer is **a. 27**.
\[
\frac{1}{3}g + 12 = 21
\]
where \( g \) is the number of games played last season.
### Step 1:
**Subtract 12 from both sides of the equation:**
\[
\frac{1}{3}g = 21 - 12
\]
\[
\frac{1}{3}g = 9
\]
### Step 2:
**Multiply both sides by 3 to solve for \( g \):**
\[
g = 9 \times 3
\]
\[
g = 27
\]
### Conclusion:
The team played **27 games** last season.
Therefore, the correct answer is **a. 27**.