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
To solve this problem, we can set up the equation:
38 + 2x = 124
Subtract 38 from both sides to isolate 2x:
2x = 86
Divide both sides by 2:
x = 43
Now we can substitute the value of x into the expression -2x - 5:
-2(43) - 5 = -86 - 5 = -91
Therefore, the answer is B) -91.
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 > 12
x > 1 2
D x < −1
To solve the inequality, we can start by distributing the 2 on the right side:
−8x + 6 ≤ -6x + 2
Next, we can add 8x to both sides and subtract 2 from both sides to isolate the variable on the left side:
6 ≤ -6x + 8x - 2
Combine like terms:
6 ≤ 2x - 2
Add 2 to both sides:
8 ≤ 2x
Finally, divide both sides by 2:
4 ≤ x
This means that all values of x that are greater than or equal to 4 satisfy the inequality.
Therefore, the answer is x ≥ 4.
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 > 12
x > 1 2
D x < −1
To solve the inequality, let's simplify each side:
−8x + 6 ≤ 2(−3x + 1)
−8x + 6 ≤ -6x + 2
Next, let's combine like terms on the right side:
-8x + 6 ≤ -6x + 2
-8x + 6 + 6x ≤ -6x + 2 + 6x
-2x + 6 ≤ 2
Now, let's isolate the x-term by subtracting 6 from both sides:
-2x + 6 - 6 ≤ 2 - 6
-2x ≤ -4
To solve for x, we need to divide both sides by -2, but remember to flip the inequality:
-2x/(-2) ≥ -4/(-2)
x ≥ 2
Therefore, the answer is x ≥ 2.
Let's break down the problem step by step:
1. The sum of 38 and twice a number x is 124.
This can be represented as: 38 + 2x = 124.
2. We need to solve for x. To do that, we isolate x by subtracting 38 from both sides of the equation:
38 + 2x - 38 = 124 - 38
2x = 86
3. Next, we need to find the value of -2x - 5.
Plugging in the value we found for x, we have:
-2(86) - 5 = -172 - 5 = -177
Therefore, the answer is (-177).
To find the value of −2x − 5, we first need to find the value of x by solving the given equation.
The equation given is: 38 + 2x = 124
To isolate x, we can subtract 38 from both sides of the equation:
2x = 124 - 38
2x = 86
Then, divide both sides of the equation by 2 to solve for x:
x = 86 / 2
x = 43
Now that we have the value of x, we can substitute it into the expression −2x − 5 to find the answer:
−2(43) − 5 = -86 - 5 = -91
Therefore, the answer is −91, which corresponds to option B.