Question

solve the equation q + 12 - 2(q - 22) > 0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation q + 12 - 2(q - 22) > 0, we need to simplify the expression and isolate the variable q.

First, distribute the -2 to the terms inside the parentheses:
q + 12 - 2q + 44 > 0

Combine like terms:
-q + 56 > 0

Now, we can isolate q by subtracting 56 from both sides of the inequality:
-q > -56

Divide both sides by -1. Since we are dividing by a negative number, we need to reverse the inequality symbol:
q < 56

Therefore, the solution to the equation is q < 56.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the inequality q + 12 - 2(q - 22) > 0 step by step, follow these steps:

Step 1: Simplify the expression inside the parentheses.
q + 12 - 2q + 44 > 0

Step 2: Simplify by combining like terms.
-q + 56 > 0

Step 3: Move the constant term to the opposite side.
-q > -56

Step 4: Multiply both sides by -1, which flips the inequality.
q < 56

Therefore, the solution to the inequality q + 12 - 2(q - 22) > 0 is q < 56.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation q + 12 - 2(q - 22) > 0, we'll follow these steps:

Step 1: Simplify the equation:
First, let's expand and simplify the expression inside the brackets:

q + 12 - 2(q - 22)
= q + 12 - 2q + 44
= -q + 56

So, our equation becomes -q + 56 > 0.

Step 2: Isolate the variable:
To isolate the variable q, we need to move all other terms to the opposite side of the inequality sign while keeping the sign direction unchanged. In our case, we'll move 56 to the opposite side by subtracting it from both sides of the inequality:

-q + 56 - 56 > 0 - 56
-q > -56

Step 3: Simplify the inequality:
To simplify the inequality, we need to change the sign of the inequality when multiplying or dividing by a negative number. In this case, we'll multiply both sides of the inequality by -1. Remember that when multiplying or dividing by a negative number, we need to flip the direction of the inequality sign:

(-1)(-q) < (-1)(-56)
q < 56

Step 4: Final solution:
The solution to the equation q + 12 - 2(q - 22) > 0 is q < 56.

Answer 4

solve the eqaution 4x + 6 < -6

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the equation 4x + 6 < -6, we'll follow these steps:

Step 1: Subtract 6 from both sides of the inequality:
4x + 6 - 6 < -6 - 6
4x < -12

Step 2: Divide both sides of the inequality by 4:
(1/4)(4x) < (-12)(1/4)
x < -3

Therefore, the solution to the equation 4x + 6 < -6 is x < -3.

Answer 6

-2/5x - 9 < 9/10

Answer 7

[AI-generated answer — Bot GPT 3.5]

To solve the inequality -2/5x - 9 < 9/10, we'll follow these steps:

Step 1: Add 9 to both sides of the inequality:
-2/5x - 9 + 9 < 9/10 + 9
-2/5x < 99/10

Step 2: Simplify the right side of the inequality:
-2/5x < 99/10

Step 3: Multiply both sides of the inequality by -5/2 (the reciprocal of -2/5) to isolate x and flip the inequality sign:
(-5/2)(-2/5x) > (-5/2)(99/10)
x > -495/20

Step 4: Simplify the right side of the inequality:
x > -2475/100
x > -24.75

Therefore, the solution to the inequality -2/5x - 9 < 9/10 is x > -24.75.