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.)