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
To solve the equation x + 0.60(15) = 0.80(x + 15), we can start by simplifying both sides of the equation:
x + 9 = 0.80x + 12
Next, we can subtract 0.80x from both sides to isolate the variable x:
x - 0.80x + 9 = 0.80x - 0.80x + 12
0.20x + 9 = 12
Next, we can subtract 9 from both sides:
0.20x + 9 - 9 = 12 - 9
0.20x = 3
To solve for x, we divide both sides by 0.20:
(0.20x)/0.20 = 3/0.20
x = 15
Therefore, the value of x is 15. The answer is D) 15.
Solve for x.
x + 0.60(15) = 0.80(x + 15)
Responses
A 99
B 1212
C 1313
D 15
To solve the equation x + 0.60(15) = 0.80(x + 15), we can start by simplifying the equation:
x + 9 = 0.80x + 12
Next, we can subtract 0.80x from both sides to isolate the variable x:
x - 0.80x + 9 = 0.80x - 0.80x + 12
0.20x + 9 = 12
Next, we can subtract 9 from both sides:
0.20x + 9 - 9 = 12 - 9
0.20x = 3
To solve for x, we divide both sides by 0.20:
(0.20x)/0.20 = 3/0.20
x = 15
Therefore, the value of x is 15. The answer is D) 15.
In the inequality, what are all the possible values of x?
2(x + 12) − 16 ≤ 8
Responses
A x < 0x < 0
B x ≤ 0x ≤ 0
C x ≥ 0x ≥ 0
D x ≤ 1x ≤ 1
To solve the inequality 2(x + 12) - 16 ≤ 8, we can start by simplifying both sides of the inequality:
2(x + 12) - 16 ≤ 8
2x + 24 - 16 ≤ 8
2x + 8 ≤ 8
Next, we can subtract 8 from both sides:
2x + 8 - 8 ≤ 8 - 8
2x ≤ 0
To solve for x, we divide both sides by 2:
(2x)/2 ≤ 0/2
x ≤ 0
Therefore, all possible values of x that satisfy the inequality are x ≤ 0. The answer is B) x ≤ 0.
Solve for x:
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
Responses
A −4−4
B −8−8
C 44
D 8
To solve the equation 4 - 2(7 + 8x) = 12 - 6(2x - 7) + 4x, we can start by simplifying both sides of the equation:
4 - 2(7 + 8x) = 12 - 6(2x - 7) + 4x
4 - 14 - 16x = 12 - 12x + 42 + 4x
Next, we can combine like terms:
-14 - 16x = 12x + 54
Next, we can move all the variables to one side and the constants to the other side:
-14 - 16x - 12x - 54 = 0
-28x - 68 = 0
Next, we can add 68 to both sides:
-28x - 68 + 68 = 0 + 68
-28x = 68
Finally, we can divide both sides by -28 to solve for x:
(-28x)/-28 = 68/-28
x = -68/28
Simplifying the fraction:
x = -17/7
Therefore, the value of x is -17/7. The answer is not provided in the given responses.
Solve for x:
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
Responses
A −4
B −8
C 4
D 8
To solve the equation 4 - 2(7 + 8x) = 12 - 6(2x - 7) + 4x, we can start by simplifying both sides of the equation:
4 - 2(7 + 8x) = 12 - 6(2x - 7) + 4x
4 - 14 - 16x = 12 - 12x + 42 + 4x
Next, we can combine like terms:
-10 - 16x = 54 - 8x
Next, we can move all the variables to one side and the constants to the other side:
-16x + 8x = 54 + 10
-8x = 64
Finally, we can divide both sides by -8 to solve for x:
(-8x)/-8 = 64/-8
x = -8
Therefore, the value of x is -8. The answer is B) -8.
In the equation, what is the value of x?
−4(x + 4x) = 2(2 − x) + 10
Responses
A −7/9
B −9/7
C 7/9
D 9/7
To solve the equation −4(x + 4x) = 2(2 − x) + 10, we can start by simplifying both sides of the equation:
−4(x + 4x) = 2(2 − x) + 10
-4(5x) = 2(2 - x) + 10
Next, we can distribute -4 and 2 to their respective terms:
-20x = 4 - 2x + 10
Next, we can combine like terms and simplify:
-20x = 14 - 2x
Now, we can subtract 14 and -2x from both sides:
-20x + 2x = 14 - 2x + 2x
-18x = 14
Finally, we can divide both sides by -18:
(-18x)/-18 = 14/-18
x = -7/9
Therefore, the value of x is -7/9. The answer is A) -7/9.
In the inequality, what are all the possible values of x?
−8x + 6 ≤ 2(−3x + 1)
Responses
A x ≥ 2x ≥ 2
B x ≤ 2x ≤ 2
C x > 1/2
D x < −1
To solve the inequality −8x + 6 ≤ 2(−3x + 1), we can start by simplifying both sides of the inequality:
-8x + 6 ≤ 2(-3x + 1)
-8x + 6 ≤ -6x + 2
Next, we can subtract 6 from both sides:
-8x + 6 - 6 ≤ -6x + 2 - 6
-8x ≤ -6x - 4
Next, we can add 6x to both sides:
-8x + 6x ≤ -6x - 4 + 6x
-2x ≤ -4
Finally, we can divide both sides by -2, remembering to reverse the inequality when dividing by a negative number:
(-2x)/-2 ≥ (-4)/-2
x ≥ 2
Therefore, all possible values of x that satisfy the inequality are x ≥ 2. The answer is A) x ≥ 2.
Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36
Given ⇒ 3(x − 4) + 5x = 9x − 36
Step 1 ⇒ 3x − 12 + 5x = 9x − 36
Step 2 ⇒ 3x + 5x − 12 = 9x − 36
Step 3 ⇒ 8x − 12 = 9x − 36
Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36
Step 5 ⇒ 0 − 12 = x − 36
Step 6 ⇒ −12 = x − 36
Step 7 ⇒ −12 + 36 = x − 36 + 36
Step 8 ⇒ 24 = x + 0
Step 9 ⇒ 24 = x
Which property yields Step 7?
Responses
A Additive Inverse PropertyAdditive Inverse Property
B Additive Identity PropertyAdditive Identity Property
C Addition Property of EqualityAddition Property of Equality
D Commutative Property of Addition
The property that yields Step 7 is the Addition Property of Equality.
In Step 7, both sides of the equation are being added by 36. According to the Addition Property of Equality, if you add the same number to both sides of an equation, the equality is still preserved.
It is given that 2(3 + x) = 6 + 2x. This is an example of the ___________ property.
Responses
A associative
B commutative
C distributive
D identity
The given equation 2(3 + x) = 6 + 2x is an example of the distributive property.
The distributive property states that for any real numbers a, b, and c, a(b + c) = ab + ac. In this equation, we have 2 as the coefficient of the parentheses, and (3 + x) is being multiplied. Using the distributive property, we can distribute the 2 to both terms inside the parentheses to get 2 * 3 + 2 * x.
Therefore, the answer is C) distributive.
The first step to solve for y in y/3
= 6 + x is
Responses
A to subtract x from both sides of the equation.to subtract x from both sides of the equation.
B to subtract y/3
from both sides of the equation.to subtract y 3 from both sides of the equation.
C to divide each term on both sides of the equation by 3.to divide each term on both sides of the equation by 3.
D to multiply each term on both sides of the equation by 3.
The first step to solve for y in y/3 = 6 + x is to multiply each term on both sides of the equation by 3.
By multiplying each term by 3, we eliminate the fraction y/3 on the left side of the equation:
3 * (y/3) = 3 * (6 + x)
y = 18 + 3x
Therefore, the first step is D) to multiply each term on both sides of the equation by 3.