The solution to the problem -4(x - 3) ≤ 16 is that x is greater than or equal to ___.
17 answers
The solution to the problem -4(x - 3) ≤ 16 is that x is greater than or equal to 7.
The solution to the problem -4(x - 3) ≤ 16 is that x is greater than or equal to ___.
Responses
A 1
B -1
Responses
A 1
B -1
The solution to the problem -4(x - 3) ≤ 16 is that x is greater than or equal to 7.
that' wrong
Apologies for the mistake. Let's solve the inequality correctly:
-4(x - 3) ≤ 16
First, we simplify the equation:
-4x + 12 ≤ 16
Next, we isolate the variable x:
-4x ≤ 4
To get rid of the negative coefficient -4, we divide both sides of the inequality by -4. Remember to reverse the inequality when dividing by a negative number:
x ≥ -1
Therefore, the correct solution to the inequality is that x is greater than or equal to -1.
-4(x - 3) ≤ 16
First, we simplify the equation:
-4x + 12 ≤ 16
Next, we isolate the variable x:
-4x ≤ 4
To get rid of the negative coefficient -4, we divide both sides of the inequality by -4. Remember to reverse the inequality when dividing by a negative number:
x ≥ -1
Therefore, the correct solution to the inequality is that x is greater than or equal to -1.
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
−4(x + 4x) = 2(2 − x) + 10
Responses
A −7/9
B −9/7
C 7/9
D 9/7
Let's solve the equation −4(x + 4x) = 2(2 − x) + 10.
First, simplify both sides of the equation:
-4(5x) = 4 - 2x + 10
-20x = -2x + 14
Next, let's isolate x by bringing all the x terms to one side and all the constant terms to the other side:
-20x + 2x = 14
-18x = 14
Now, divide both sides of the equation by -18:
x = 14 / -18
Simplifying the fraction,
x = -7/9
Therefore, the value of x in the equation is -7/9.
So, the correct option is A. −7/9.
First, simplify both sides of the equation:
-4(5x) = 4 - 2x + 10
-20x = -2x + 14
Next, let's isolate x by bringing all the x terms to one side and all the constant terms to the other side:
-20x + 2x = 14
-18x = 14
Now, divide both sides of the equation by -18:
x = 14 / -18
Simplifying the fraction,
x = -7/9
Therefore, the value of x in the equation is -7/9.
So, the correct option is A. −7/9.
The sum of 38 and twice a number x is 124. What is −2x − 5?
Responses
A −101
B −91
C 46
D 86
Responses
A −101
B −91
C 46
D 86
Let's solve the equation to find the value of x:
38 + 2x = 124
Subtract 38 from both sides:
2x = 124 - 38
2x = 86
Next, divide both sides by 2 to solve for x:
x = 86 / 2
x = 43
Now, substitute the value of x into the expression -2x - 5:
-2(43) - 5 = -86 - 5 = -91
Therefore, the correct answer is option B: -91.
38 + 2x = 124
Subtract 38 from both sides:
2x = 124 - 38
2x = 86
Next, divide both sides by 2 to solve for x:
x = 86 / 2
x = 43
Now, substitute the value of x into the expression -2x - 5:
-2(43) - 5 = -86 - 5 = -91
Therefore, the correct answer is option B: -91.
Solve for x:
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
Responses
A −4−4
B −8−8
C 44
D 8
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
Responses
A −4−4
B −8−8
C 44
D 8
Let's solve the equation step by step:
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
First, simplify both sides of the equation:
4 - 14 - 16x = 12 - 12x + 42 + 4x
Combine like terms on each side:
-10 - 16x = 54 - 8x
Next, subtract 54 from both sides:
-10 - 16x - 54 = -8x
-64 - 16x = -8x
To eliminate the x term on the left side, add 16x to both sides:
-64 = 8x - 8x
-64 = 0
This equation is inconsistent and has no solution.
Therefore, there is no value of x that satisfies the equation.
The correct answer is: No solution.
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
First, simplify both sides of the equation:
4 - 14 - 16x = 12 - 12x + 42 + 4x
Combine like terms on each side:
-10 - 16x = 54 - 8x
Next, subtract 54 from both sides:
-10 - 16x - 54 = -8x
-64 - 16x = -8x
To eliminate the x term on the left side, add 16x to both sides:
-64 = 8x - 8x
-64 = 0
This equation is inconsistent and has no solution.
Therefore, there is no value of x that satisfies the equation.
The correct answer is: No solution.
Solve for x:
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
Responses
A −4
B −8
C 4
D 8
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
Responses
A −4
B −8
C 4
D 8
To solve for x in the equation 4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x, let's simplify step by step:
First, distribute -2 and -6 to their respective terms:
4 - 14 - 16x = 12 - 12x + 42 + 4x
Simplify further:
-10 -16x = 54 - 8x + 4x
Combine like terms:
-10 - 16x = 54 - 4x
To eliminate the x-term on the right side, we add 4x to both sides:
-10 - 16x + 4x = 54 - 4x + 4x
Simplifying:
-10 - 12x = 54
To isolate the x-term, we subtract -10 from both sides:
-10 - 12x - (-10) = 54 - (-10)
Simplifying:
-12x = 64
Next, we divide both sides by -12 to solve for x:
x = 64 / -12
Simplifying the fraction:
x = -16/3
Therefore, the value of x in the equation is -16/3.
So, the correct answer is not listed among the provided options.
First, distribute -2 and -6 to their respective terms:
4 - 14 - 16x = 12 - 12x + 42 + 4x
Simplify further:
-10 -16x = 54 - 8x + 4x
Combine like terms:
-10 - 16x = 54 - 4x
To eliminate the x-term on the right side, we add 4x to both sides:
-10 - 16x + 4x = 54 - 4x + 4x
Simplifying:
-10 - 12x = 54
To isolate the x-term, we subtract -10 from both sides:
-10 - 12x - (-10) = 54 - (-10)
Simplifying:
-12x = 64
Next, we divide both sides by -12 to solve for x:
x = 64 / -12
Simplifying the fraction:
x = -16/3
Therefore, the value of x in the equation is -16/3.
So, the correct answer is not listed among the provided options.
that's wrong
Apologies for the mistake. Let's solve the equation correctly:
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
First, simplify the expressions inside the parentheses:
4 - 2(7) - 2(8x) = 12 - 6(2x) + 6(7) + 4x
Simplify further:
4 - 14 - 16x = 12 - 12x + 42 + 4x
Combine like terms on each side:
-10 - 16x = 54 - 8x + 4x
To isolate the x terms on one side and the constant terms on the other side, let's subtract 54 and add 16x to both sides:
-10 - 16x - 54 + 16x = 54 - 8x + 4x - 54 + 16x
Simplify:
-64 = 8x
Finally, divide both sides by 8 to solve for x:
x = -64 / 8
Simplify the fraction:
x = -8
Therefore, the correct response is option B: -8.
4 − 2(7 + 8x) = 12 − 6(2x − 7) + 4x
First, simplify the expressions inside the parentheses:
4 - 2(7) - 2(8x) = 12 - 6(2x) + 6(7) + 4x
Simplify further:
4 - 14 - 16x = 12 - 12x + 42 + 4x
Combine like terms on each side:
-10 - 16x = 54 - 8x + 4x
To isolate the x terms on one side and the constant terms on the other side, let's subtract 54 and add 16x to both sides:
-10 - 16x - 54 + 16x = 54 - 8x + 4x - 54 + 16x
Simplify:
-64 = 8x
Finally, divide both sides by 8 to solve for x:
x = -64 / 8
Simplify the fraction:
x = -8
Therefore, the correct response is option B: -8.
In the inequality, what are all the possible values of x?
−8x + 6 ≤ 2(−3x + 1)
Responses
A x ≥ 2
B x ≤ 2
C x > 12
D x < −1
−8x + 6 ≤ 2(−3x + 1)
Responses
A x ≥ 2
B x ≤ 2
C x > 12
D x < −1
Let's solve the inequality step by step:
−8x + 6 ≤ 2(−3x + 1)
First, distribute 2 to -3x and 1:
−8x + 6 ≤ -6x + 2
Next, let's isolate x by bringing all x terms to one side and constant terms to the other side:
−8x + 6x ≤ 2 - 6
-2x ≤ -4
Now, divide both sides of the inequality by -2. Remember to reverse the inequality when dividing by a negative number:
x ≥ 2
Therefore, all the possible values of x are greater than or equal to 2.
The correct response is option A: x ≥ 2.
−8x + 6 ≤ 2(−3x + 1)
First, distribute 2 to -3x and 1:
−8x + 6 ≤ -6x + 2
Next, let's isolate x by bringing all x terms to one side and constant terms to the other side:
−8x + 6x ≤ 2 - 6
-2x ≤ -4
Now, divide both sides of the inequality by -2. Remember to reverse the inequality when dividing by a negative number:
x ≥ 2
Therefore, all the possible values of x are greater than or equal to 2.
The correct response is option A: x ≥ 2.