Solve the equation. Check your solution.
2x + 6x - 7 = 9
x = [ ] (Simplify your answer.)
To solve the equation 2x + 6x - 7 = 9, we first combine like terms:
2x + 6x - 7 = 9
8x - 7 = 9
Next, we isolate the variable by adding 7 to both sides:
8x - 7 + 7 = 9 + 7
8x = 16
Finally, we solve for x by dividing both sides by 8:
8x/8 = 16/8
x = 2
To check the solution, we substitute x = 2 back into the original equation:
2(2) + 6(2) - 7 = 9
4 + 12 - 7 = 9
16 - 7 = 9
9 = 9
Since the equation is true, the solution x = 2 is correct.
Solve the equation. Check your answer.
24 = 5x + 6 - 2x
x = [ ]
To solve the equation 24 = 5x + 6 - 2x, we combine like terms:
24 = 3x + 6
Next, we isolate the variable by subtracting 6 from both sides:
24 - 6 = 3x + 6 - 6
18 = 3x
Finally, we solve for x by dividing both sides by 3:
18/3 = 3x/3
6 = x
To check the solution, we substitute x = 6 back into the original equation:
24 = 5(6) + 6 - 2(6)
24 = 30 + 6 - 12
24 = 36 - 12
24 = 24
Since the equation is true, the solution x = 6 is correct.
Solve the equation.
7(3x - 2) = 28
x [ ] (Simplify your answer.)
To solve the equation 7(3x - 2) = 28, we first distribute the 7 to the terms inside the parentheses:
21x - 14 = 28
Next, we isolate the variable by adding 14 to both sides:
21x - 14 + 14 = 28 + 14
21x = 42
Finally, we solve for x by dividing both sides by 21:
21x/21 = 42/21
x = 2
Therefore, the solution to the equation is x = 2.
Solve the equation. Check your answer.
-2(r + 9) = -31
r = [ ] (Simplify your answer. Type an integer or a fraction.)
To solve the equation -2(r + 9) = -31, we first distribute the -2 to the terms inside the parentheses:
-2r - 18 = -31
Next, we isolate the variable by adding 18 to both sides:
-2r - 18 + 18 = -31 + 18
-2r = -13
Finally, we solve for r by dividing both sides by -2:
(-2r)/-2 = -13/-2
r = 6.5
Therefore, the solution to the equation is r = 6.5.
To check the solution, we substitute r = 6.5 back into the original equation:
-2(6.5 + 9) = -31
-2(15.5) = -31
-31 = -31
Since the equation is true, the solution r = 6.5 is correct.
Solve the equation. Choose the method you prefer to use. Check your answer.
b / 13 - 6b / 13 = 40 / 13
b = [ ] (Simplify your answer.)
To solve the equation b / 13 - 6b / 13 = 40 / 13, we can simplify the left side of the equation by combining the fractions:
(b - 6b) / 13 = 40 / 13
Simplifying further, we have:
-5b / 13 = 40 / 13
To isolate the variable b, we multiply both sides of the equation by 13:
(13)(-5b / 13) = (13)(40 / 13)
-5b = 40
Next, we solve for b by dividing both sides of the equation by -5:
-5b / -5 = 40 / -5
b = -8
To check the solution, we substitute b = -8 back into the original equation:
(-8) / 13 - 6(-8) / 13 = 40 / 13
-8/13 + 48/13 = 40/13
(48 - 8) / 13 = 40 / 13
40 / 13 = 40 / 13
Since the equation is true, the solution b = -8 is correct.
Solve the equation below. Choose the method you prefer to use. Check your answer.
n / 7 - 9n / 14 = 1 / 7
n = [ ] (Type an integer or a simplified fraction.)
To solve the equation n / 7 - 9n / 14 = 1 / 7, we can find a common denominator for the fractions on the left side, which is 14:
(2n / 14) - (9n / 14) = 1 / 7
Next, we can combine the fractions on the left side:
(2n - 9n) / 14 = 1 / 7
Simplifying further, we have:
(-7n) / 14 = 1 / 7
Now, we can simplify the left side of the equation by dividing both the numerator and denominator by 7:
(-n) / 2 = 1 / 7
To remove the fraction, we can multiply both sides of the equation by 2:
(2)(-n) / 2 = (1 / 7)(2)
-n = 2 / 7
Next, we multiply both sides of the equation by -1 to isolate the variable:
(-1)(-n) = (-1)(2 / 7)
n = -2 / 7
Therefore, the solution to the equation is n = -2 / 7.
To check the solution, we substitute n = -2 / 7 back into the original equation:
(-2 / 7) / 7 - 9(-2 / 7) / 14 = 1 / 7
-2 / 49 + 9(2 / 7) / 14 = 1 / 7
-2 / 49 + 18 / 98 = 1 / 7
(-2)(2) / (49)(2) + 18 / 98 = 1 / 7
-4 / 98 + 18 / 98 = 1 / 7
(-4 + 18) / 98 = 1 / 7
14 / 98 = 1 / 7
1 / 7 = 1 / 7
Since the equation is true, the solution n = -2 / 7 is correct.
Solve the equation.
8n - (4n + 5) = 7
n = [ ] (Simplify your answer.)
To solve the equation 8n - (4n + 5) = 7, we first simplify by distributing the negative sign to the terms within the parentheses:
8n - 4n - 5 = 7
Next, we combine like terms:
4n - 5 = 7
Then, we isolate the variable by adding 5 to both sides:
4n - 5 + 5 = 7 + 5
4n = 12
Finally, we solve for n by dividing both sides by 4:
4n/4 = 12/4
n = 3
Therefore, the solution to the equation is n = 3.
Angie and Kenny play online video games. Angie buys 1 software package and 4 months of gameplay. Kenny buys 1 software and 2 months of gameplay. Each software package costs $35. If their total cost is $148, what is the cost of one month of game play?
The cost of one month of game play is $ [ ] (Type an integer or a decimal.)
Let's denote the cost of one month of gameplay as "x".
Angie's total cost is the cost of the software package plus 4 times the cost of one month of gameplay, so her total cost is 35 + 4x.
Kenny's total cost is the cost of the software package plus 2 times the cost of one month of gameplay, so his total cost is 35 + 2x.
We know that their total cost combined is $148, so we can set up the equation:
35 + 4x + 35 + 2x = 148
Combining like terms:
6x + 70 = 148
Subtracting 70 from both sides:
6x = 78
Dividing both sides by 6:
x = 13
Therefore, the cost of one month of gameplay is $13.
Solve.
12x + 11 = 5x - 13
x = [ ] (Simplify your answer. Type an integer or a fraction.)
To solve the equation 12x + 11 = 5x - 13, we will isolate the variable x.
First, we can simplify the equation by moving all terms with x to one side:
12x - 5x = -13 - 11
This simplifies to:
7x = -24
Next, we solve for x by dividing both sides of the equation by 7:
7x/7 = -24/7
This further simplifies to:
x = -24/7
So, the solution to the equation is x = -24/7.
that was incorrect
Apologies for the incorrect response.
Let's solve the equation again:
To solve the equation 12x + 11 = 5x - 13, we will isolate the variable x.
To do this, we will move all the terms with x to one side and the constant terms to the other side:
12x - 5x = -13 - 11
Simplifying, we have:
7x = -24
Next, we solve for x by dividing both sides of the equation by 7:
7x/7 = -24/7
Simplifying further, we have:
x = -24/7
Therefore, the solution to the equation is x = -24/7.
thats the same answer that was incorrect
Apologies for the confusion. Let's solve the equation correctly this time:
To solve the equation 12x + 11 = 5x - 13, we will isolate the variable x.
First, let's get all the terms with x on one side by subtracting 5x from both sides:
12x - 5x + 11 = 5x - 5x - 13
Simplifying, we get:
7x + 11 = -13
Next, let's isolate x by subtracting 11 from both sides:
7x + 11 - 11 = -13 - 11
Simplifying further, we have:
7x = -24
Finally, we can solve for x by dividing both sides by 7:
7x/7 = -24/7
This simplifies to:
x = -24/7
Therefore, the correct solution to the equation is x = -24/7.
Solve the equation. Check your solution.
4y - 2 = 33 - 3y
y = [ ]
To solve the equation 4y - 2 = 33 - 3y, we will isolate the variable y.
First, let's simplify the equation by combining like terms:
4y + 3y = 33 + 2
This simplifies to:
7y = 35
Next, divide both sides of the equation by 7 to solve for y:
7y/7 = 35/7
Simplifying further, we have:
y = 5
Therefore, the solution to the equation is y = 5.
To check the solution, substitute y = 5 back into the original equation:
4(5) - 2 = 33 - 3(5)
20 - 2 = 33 - 15
18 = 18
Since the equation is true, the solution y = 5 is correct.
Solve the equation. Check your solution.
-4y + 6 = 23y - 3
y = [ ] (Type an integer or a simplified fraction.)
To solve the equation -4y + 6 = 23y - 3, we will isolate the variable y.
First, let's simplify the equation by combining like terms:
-4y - 23y = -3 - 6
This simplifies to:
-27y = -9
Next, divide both sides of the equation by -27 to solve for y:
(-27y)/(-27) = (-9)/(-27)
Simplifying further, we have:
y = 1/3
Therefore, the solution to the equation is y = 1/3.
To check the solution, substitute y = 1/3 back into the original equation:
-4(1/3) + 6 = 23(1/3) - 3
-4/3 + 6 = 23/3 - 3
18/3 - 4/3 = 23/3 - 3
14/3 = 14/3
Since the equation is true, the solution y = 1/3 is correct.
Solve the equation. Check your answer.
10(x - 5) = 9(x+5)
x = [ ] (Type an integer or a simplified fraction.)
To solve the equation 10(x - 5) = 9(x + 5), we will distribute and simplify on both sides:
10x - 50 = 9x + 45
Next, we will isolate the variable x by subtracting 9x from both sides:
10x - 9x - 50 = 9x - 9x + 45
This simplifies to:
x - 50 = 45
Next, we will add 50 to both sides to further isolate the variable x:
x - 50 + 50 = 45 + 50
This simplifies to:
x = 95
Therefore, the solution to the equation is x = 95.
To check the solution, substitute x = 95 back into the original equation:
10(95 - 5) = 9(95 + 5)
10(90) = 9(100)
900 = 900
Since the equation is true, the solution x = 95 is correct.
Determine whether the equation is an identity or whether it has no solution.
4(a - 3) = 8a - (4a - 12)
To determine whether the equation 4(a - 3) = 8a - (4a - 12) is an identity or has no solution, we will simplify and compare both sides.
First, let's simplify both sides of the equation:
4(a - 3) = 8a - (4a - 12)
4a - 12 = 8a - 4a + 12
Next, combine like terms:
4a - 12 = 4a + 12
Now, let's subtract 4a from both sides:
-12 = 12
The equation -12 = 12 is not true. Therefore, there is no solution to the equation.
In conclusion, the equation 4(a - 3) = 8a - (4a - 12) has no solution.
Determine whether the equation below is an identity or whether it has no solution.
-3(6x - 7) = -18x + 21
Choose the correct answer below.
The correct answer is that the equation -3(6x - 7) = -18x + 21 is an identity.
To demonstrate this, let's simplify both sides of the equation:
-3(6x - 7) = -18x + 21
-18x + 21 = -18x + 21
As we can see, both sides of the equation are equal, and the equation holds true for all values of x. Therefore, it is an identity.
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $74. A season ski pass costs $300. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
The skier would have to go skiing [ ] days. (Type a whole number.)
Let's analyze the cost of skiing for both options: daily passes and season pass.
For daily passes, the skier pays $74 per day plus an additional $20 for ski rentals. Therefore, the cost per day with daily passes is $74 + $20 = $94.
For the season pass, the skier pays a flat fee of $300 for unlimited skiing. However, they still have to pay $20 per day for ski rentals.
To determine how many days the skier would need to go skiing for the season pass to be less expensive than the daily passes, we can set up the following equation:
$94 * D = $300 + $20 * D
Where D represents the number of days the skier would need to go skiing.
Now, we can solve for D:
$94 * D = $300 + $20 * D
$94D - $20D = $300
$74D = $300
D = $300 / $74
Simplifying this division, we find:
D ≈ 4.05
Since D represents the number of days skiing, it must be a whole number. Thus, the skier would need to go skiing for at least 5 days in order for the season pass