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

Answer 1

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

solve the eqaution 4x + 6 < -6

Answer 3

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 4

-2/5x - 9 < 9/10

Answer 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.