Sure! Let's solve these equations step by step.
Question 1: Solve the inequality -2/5x - 9 < 9/10
Step 1: To solve this inequality, we'll start by isolating the variable x. Let's begin:
-2/5x - 9 < 9/10
Step 2: To eliminate the fraction, we'll multiply both sides of the inequality by the common denominator of 10:
10 * (-2/5x - 9) < 10 * (9/10)
-4x - 90 < 9
Step 3: Now, let's isolate x by moving the constant term (-90) to the other side of the inequality:
-4x < 9 + 90
-4x < 99
Step 4: To solve for x, divide both sides of the inequality by -4. However, keep in mind that when we divide both sides of an inequality by a negative number, the direction of the inequality sign flips.
x > 99 / -4 (Remember to change the direction of the inequality)
x > -24.75
So, the solution to the inequality is x > -24.75.
Question 2: Solve the inequality 4x + 6 < -6
Step 1: To solve this inequality, we'll start by isolating the variable x. Let's begin:
4x + 6 < -6
Step 2: Now, let's isolate x by moving the constant term (6) to the other side of the inequality:
4x < -6 - 6
4x < -12
Step 3: To solve for x, divide both sides of the inequality by 4:
x < -12 / 4
x < -3
So, the solution to the inequality is x < -3.
Question 3: Solve the inequality q + 12 - 2(q - 22) > 0
Step 1: Let's start by simplifying the expression inside the brackets first:
q + 12 - 2q + 44 > 0
Step 2: Combine like terms:
-q + 56 > 0
Step 3: Now, let's isolate q by moving the constant term (56) to the other side of the inequality:
-q > -56
Step 4: To solve for q, divide both sides of the inequality by -1. Remember, when you divide both sides by a negative number, the direction of the inequality sign flips:
q < -56
So, the solution to the inequality is q < -56.
I hope this helps! Let me know if you have any other questions.