Solve the following inequality for hh. Write your answer in simplest form.
minus, 5, h, minus, left bracket, h, plus, 2, right bracket, is greater than or equal to, 5, h, plus, 8, plus, 6
−5h−(h+2)≥
5h+8+6
Simplifying both sides of the inequality:
-5h - (h + 2) ≥ 5h + 14
Expanding:
-5h - h - 2 ≥ 5h + 14
Combining like terms:
-6h - 2 ≥ 5h + 14
Adding 6h to both sides:
-2 ≥ 11h + 14
Subtracting 14 from both sides:
-16 ≥ 11h
Dividing both sides by 11:
-16/11 ≥ h
Simplifying the fraction:
-1.45 ≥ h
In simplest form, h ≥ -1.45
To solve the inequality, we can follow these steps:
Step 1: Simplify both sides of the inequality by distributing the negative sign in front of the parentheses on the left side and combining like terms on both sides.
-5h - h - 2 ≥ 5h + 14
Step 2: Combine like terms on both sides of the inequality.
-6h - 2 ≥ 5h + 14
Step 3: Move all terms containing h to one side of the inequality by subtracting 5h from both sides.
-6h - 5h - 2 ≥ 14
-11h - 2 ≥ 14
Step 4: Move the constant term to the other side of the inequality by adding 2 to both sides.
-11h ≥ 14 + 2
-11h ≥ 16
Step 5: Divide both sides of the inequality by -11 (remember to reverse the inequality sign when dividing by a negative number).
h ≤ 16/-11
h ≤ -16/11
Therefore, the solution to the inequality -5h - (h+2) ≥ 5h + 8 + 6 is h ≤ -16/11.
To solve the inequality, we will simplify and then isolate the variable "h" on one side. Here are the steps to follow:
1. Simplify both sides of the inequality:
Start by distributing the negative sign (-) to the terms within the parentheses on the left side:
-5h - h - 2 ≥ 5h + 14
Combine like terms:
-6h - 2 ≥ 5h + 14
2. Move all terms containing "h" to one side:
Add 6h to both sides of the inequality:
-6h + 6h - 2 ≥ 5h + 6h + 14
Simplify:
-2 ≥ 11h + 14
3. Move all constant terms to the other side:
Subtract 14 from both sides of the inequality:
-2 - 14 ≥ 11h + 14 - 14
Simplify:
-16 ≥ 11h
4. Divide both sides of the inequality by 11:
Divide -16 by 11, remembering to flip the inequality sign since we are dividing by a negative value:
-16/11 ≤ (11h)/11
Simplify:
-16/11 ≤ h
Alternatively, you can write it as:
h ≥ -16/11
Therefore, the solution to the inequality is h ≥ -16/11 in simplest form.