27x + 14 = 3(9x - 7)
Responses
A x = 0x = 0
B x = −35x = −35
C no solutionno solution
D x = 0 or x = −35x = 0 or x = −35
E infinitely many solutions
To solve the equation 27x + 14 = 3(9x - 7), we can start by distributing the 3 to both terms in the parentheses:
27x + 14 = 27x - 21
Next, we can subtract 27x from both sides to isolate the constant term:
14 = -21
This statement is not true, so there are no solutions to the equation. Therefore, the answer is C) no solution.
Solve the equation for x.
2/5 (2x − 12) = −28
Responses
A −18−18
B −29−29
C −32−32
D −9
To solve the equation 2/5 (2x - 12) = -28, we can start by distributing 2/5 to both terms in the parentheses:
(2/5) * 2x - (2/5) * 12 = -28
4/5 * x - 24/5 = -28
Next, we can add 24/5 to both sides to isolate the variable x:
4/5 * x = -28 + 24/5
4/5 * x = -140/5 + 24/5
4/5 * x = -116/5
To get rid of the fraction, we multiply both sides by the reciprocal of 4/5, which is 5/4:
(5/4) * (4/5) * x = (5/4) * (-116/5)
1 * x = -580/20
x = -29
Therefore, the solution to the equation is x = -29. The answer is B) -29.
The sum of 38 and twice a number x is 124. What is −2x − 5?
Responses
A −101−101
B −91−91
C 4646
D 86
We are given that the sum of 38 and twice a number x is 124. We can represent this as an equation:
38 + 2x = 124
Next, we can subtract 38 from both sides:
2x = 124 - 38
2x = 86
To solve for x, we divide both sides by 2:
x = 86/2
x = 43
Now, we can plug this value back into the expression -2x - 5:
-2(43) - 5 = -86 - 5 = -91
Therefore, the value of -2x - 5 is -91. The answer is B) -91.
What is the value of x, when 10(x + 2) = 5(x + 8)?
Responses
A x = 1x = 1
B x = 2x = 2
C x = 4x = 4
D x = 5/6
E x = 2/23
To solve the equation 10(x + 2) = 5(x + 8), we start by distributing 10 to both terms inside the parentheses and also distribute 5 to both terms inside the parentheses:
10x + 20 = 5x + 40
Next, we can subtract 5x from both sides to isolate the variable x:
10x - 5x + 20 = 5x - 5x + 40
5x + 20 = 40
Next, we can subtract 20 from both sides:
5x + 20 - 20 = 40 - 20
5x = 20
To solve for x, we divide both sides by 5:
(5x)/5 = 20/5
x = 4
Therefore, the value of x is 4. The answer is C) x = 4.
Solve for x:
x(8 + 2) + 3 = 2(5 + x) + 5(x + 1) − 6
Responses
A −4−4
B −2−2
C 22
D 4
To solve the equation x(8 + 2) + 3 = 2(5 + x) + 5(x + 1) - 6, we can start by simplifying both sides of the equation:
x(10) + 3 = 2(5 + x) + 5(x + 1) - 6
10x + 3 = 10 + 2x + 5x + 5 - 6
Next, we can combine like terms:
10x + 3 = 7x + 9
Next, we can subtract 7x from both sides to isolate the variable x:
10x - 7x + 3 = 7x - 7x + 9
3x + 3 = 9
Next, we can subtract 3 from both sides:
3x + 3 - 3 = 9 - 3
3x = 6
To solve for x, we divide both sides by 3:
(3x)/3 = 6/3
x = 2
Therefore, the value of x is 2. The answer is B) x = 2.
Solve for x.
x + 0.60(15) = 0.80(x + 15)
Responses
A 99
B 12
C 13
D 15