The sum of 38 and twice a number x is 124. What is −2x − 5?

Question

Responses
A −101−101
B −91−91
C 4646
D 86

Answer 1

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.

Answer 2

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

Answer 3

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.

Answer 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

Answer 5

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.