IM SO CONFUSED

To solve this inequality,* you first need to simplify the left side. *

You can do this by first applying the distributive property; you will distribute the coefficients outside of the parentheses to the terms inside the parentheses through multiplication.

For the first set of parentheses you multiply -3 by X and by 1. Your result will be -3x and -3. Since you have distributed, you can eliminate the parentheses.

**Your inequality now reads 1-3x -3 +7(x-6)>0**

Let's use the distributive property on the second parentheses. Multiply 7 by X and -6. Your result is 7x - 42. Again, you can eliminate the parentheses.

**Your inequality now reads 1-3x-3+7x-42>0**

The next step is to* combine your like terms*. Like terms are terms that have the same variable and the same degree (exponent).

The like terms on the left side are the constants: 1, -3, and -42. Let's combine the negative integers first. -42 and -3 make -45. Add 1 and your result is -44

**You can rewrite the inequality to read -3x +7x - 44 >0**

**
**Now combine the remaining like terms: -3x and 7x. The commutative property allows us to switch the order of these terms without changing the result:
7x -3x. The result is 4x.

**Your inequality now reads 4x -44 >0**

Almost there! We want to solve for the variable x, so we need to isolate it, or get it by itself on one side of the inequality. To do that,
*we will use inverse operations to "undo" what is happening to the x. *

X is being multiplied by 4 and X is subtracting 44.

To "undo" subtracting 44, you should add 44 to both sides of the inequality. 4x -44** + 44** > 0
**+ 44. **The constants eliminate each other on the left, and the right side becomes 44.

**4x > 44**

**
**X is being multiplied by 4. To "undo" multiplying by 4, you should divide both sides of the inequality by 4.

4x **/4** > 44**/4** =

**x > 11**

This is your solution set. To check your work, substitute a value greater than 11 into your inequality. If the inequality is true, values than 11 work. You should also substitute a value less than 11 into your inequality. That should make the inequality false.

Check: Let x = 20

1 - 3(12+1) + 7(12-6) > 0 =

1 - 3(13) + 7(6) > 0 =

1- 39 + 42 > 0 =

-38 + 42 > 0 =

4 > 0 is true, so x can be greater than 11.

Check: Let x = 10

1 -3(10+1) + 7(10-6) >0 =

1- 3(11) + 7(4) > 0 =

1 - 33 + 28 > 0 =

-32 + 28 > 0 =

-4 > 0 is not true. Therefore, x cannot be less than 11.

I hope this helped!