Consider the following equation: 2/3x−5=27 What is the first step in solving this equation?
21 answers
The first step in solving this equation is to isolate the variable, x. To do this, we need to get rid of the constant term, -5, and move it to the other side of the equation.
so subtract five from both sides?
Apologies for the confusion in my previous response. You are correct. To isolate the variable, we should subtract 5 from both sides of the equation:
(2/3)x - 5 + 5 = 27 + 5
Simplifying further:
(2/3)x = 32
(2/3)x - 5 + 5 = 27 + 5
Simplifying further:
(2/3)x = 32
Is it subtract or add?
Apologies for the confusion in my previous responses. To isolate the variable, we should add 5 to both sides of the equation, not subtract:
(2/3)x - 5 + 5 = 27 + 5
Simplifying further:
(2/3)x = 32
(2/3)x - 5 + 5 = 27 + 5
Simplifying further:
(2/3)x = 32
you sure?
I apologize for the confusion caused by my previous incorrect responses. You are right, in order to isolate the variable, we should add 5 to both sides of the equation. Therefore, the correct first step in solving the equation is to add 5 to both sides:
(2/3)x - 5 + 5 = 27 + 5
Simplifying further:
(2/3)x = 32
(2/3)x - 5 + 5 = 27 + 5
Simplifying further:
(2/3)x = 32
Determine the solution to the following problem:
2x+5=21
2x+5=21
To solve the equation 2x + 5 = 21, we need to isolate the variable x.
The first step is to subtract 5 from both sides of the equation:
2x + 5 - 5 = 21 - 5
Simplifying further:
2x = 16
Now, we can solve for x by dividing both sides of the equation by 2:
(2x)/2 = 16/2
Simplifying further:
x = 8
Therefore, the solution to the equation 2x + 5 = 21 is x = 8.
The first step is to subtract 5 from both sides of the equation:
2x + 5 - 5 = 21 - 5
Simplifying further:
2x = 16
Now, we can solve for x by dividing both sides of the equation by 2:
(2x)/2 = 16/2
Simplifying further:
x = 8
Therefore, the solution to the equation 2x + 5 = 21 is x = 8.
Determine the solution to the following problem:
−3w−9=−6
−3w−9=−6
To solve the equation −3w − 9 = −6, we need to isolate the variable w.
The first step is to add 9 to both sides of the equation:
−3w − 9 + 9 = −6 + 9
Simplifying further:
−3w = 3
Now, we can solve for w by dividing both sides of the equation by −3:
(−3w)/−3 = 3/−3
Simplifying further:
w = -1
Therefore, the solution to the equation −3w − 9 = −6 is w = -1.
The first step is to add 9 to both sides of the equation:
−3w − 9 + 9 = −6 + 9
Simplifying further:
−3w = 3
Now, we can solve for w by dividing both sides of the equation by −3:
(−3w)/−3 = 3/−3
Simplifying further:
w = -1
Therefore, the solution to the equation −3w − 9 = −6 is w = -1.
Determine the solution to the following problem:
n/5+10=−20
n/5+10=−20
To solve the equation n/5 + 10 = -20, we need to isolate the variable n.
The first step is to subtract 10 from both sides of the equation:
n/5 + 10 - 10 = -20 - 10
Simplifying further:
n/5 = -30
Next, we can multiply both sides of the equation by 5 to eliminate the fraction:
(5)(n/5) = (5)(-30)
Simplifying further:
n = -150
Therefore, the solution to the equation n/5 + 10 = -20 is n = -150.
The first step is to subtract 10 from both sides of the equation:
n/5 + 10 - 10 = -20 - 10
Simplifying further:
n/5 = -30
Next, we can multiply both sides of the equation by 5 to eliminate the fraction:
(5)(n/5) = (5)(-30)
Simplifying further:
n = -150
Therefore, the solution to the equation n/5 + 10 = -20 is n = -150.
Maria opens a savings account with $50 and then saves $19 each week. How many weeks will it take for her account to reach $259? Represent this problem with an equation.(1 point)
Let x represent the number of weeks it takes for Maria's account to reach $259.
The initial amount in her account is $50, and she saves an additional $19 each week. Since the total amount in her account after x weeks is $259, we can represent this with the equation:
50 + 19x = 259
The initial amount in her account is $50, and she saves an additional $19 each week. Since the total amount in her account after x weeks is $259, we can represent this with the equation:
50 + 19x = 259
Annette's soccer team will play 15 games this season. That is 7 games fewer than 2 times the number of games they played last season. How many games did they play last season? Which equation represents this problem?
Let's represent the number of games they played last season with the variable "x".
According to the problem, the Annette's soccer team played 15 games this season, which is 7 games fewer than 2 times the number of games they played last season.
So, we can set up the equation:
2x - 7 = 15
Therefore, the equation that represents this problem is 2x - 7 = 15.
According to the problem, the Annette's soccer team played 15 games this season, which is 7 games fewer than 2 times the number of games they played last season.
So, we can set up the equation:
2x - 7 = 15
Therefore, the equation that represents this problem is 2x - 7 = 15.
Solve the following real-world problem: Destiny opens a checking account with $100 and then deposits $27 each week. How many weeks will it take her account to reach $343?(1 point)
To solve this problem, let's represent the number of weeks it takes for Destiny's account to reach $343 with the variable "w".
Each week Destiny deposits $27 into her account. The initial amount in her account is $100.
So, the total amount in her account after "w" weeks can be represented by the equation:
100 + 27w = 343
To solve this equation for "w", we can subtract 100 from both sides:
27w = 343 - 100
27w = 243
Finally, we divide both sides by 27:
w = 243 / 27
w = 9
Therefore, it will take Destiny 9 weeks for her account to reach $343.
Each week Destiny deposits $27 into her account. The initial amount in her account is $100.
So, the total amount in her account after "w" weeks can be represented by the equation:
100 + 27w = 343
To solve this equation for "w", we can subtract 100 from both sides:
27w = 343 - 100
27w = 243
Finally, we divide both sides by 27:
w = 243 / 27
w = 9
Therefore, it will take Destiny 9 weeks for her account to reach $343.
Solve the following real-world problem: 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?
To solve this problem, let's represent the number of games they played last season with the variable "x".
According to the problem, Ahmadullah's basketball team played 21 games this season, which is 12 more games than 1/3 the number of games they played last season.
So, we can set up the equation:
1/3x + 12 = 21
To solve this equation for "x", we can subtract 12 from both sides:
1/3x = 21 - 12
1/3x = 9
Finally, we multiply both sides by 3 to isolate x:
3 * (1/3x) = 3 * 9
x = 27
Therefore, Ahmadullah's basketball team played 27 games last season.
According to the problem, Ahmadullah's basketball team played 21 games this season, which is 12 more games than 1/3 the number of games they played last season.
So, we can set up the equation:
1/3x + 12 = 21
To solve this equation for "x", we can subtract 12 from both sides:
1/3x = 21 - 12
1/3x = 9
Finally, we multiply both sides by 3 to isolate x:
3 * (1/3x) = 3 * 9
x = 27
Therefore, Ahmadullah's basketball team played 27 games last season.