Solving an inequality is a process of finding the values of a variable that makes the inequality true. This means that the solution is the set of values of the variable that satisfies the inequality. In this article, we will discuss how to solve the inequality 3b-7 32.
Step 1: Simplify the Inequality
The first step in solving an inequality is to simplify the expression. In this case, we need to use the distributive property to expand the expression. The distributive property states that when multiplying a number by a sum or difference of two numbers, the number can be distributed to each of the terms in the sum or difference. Thus, the expression 3b-7 32 can be simplified to 3b -7 + 32. To solve the inequality, we will need to rearrange the terms to make the variable, b, the subject.
Step 2: Isolate the Variable
In order to isolate the variable, we need to move all terms that are not related to the variable to one side of the inequality sign. Since b is on the left side of the inequality sign, we will move all terms on the right side of the inequality sign to the left side of the sign. To do this, we will need to use addition and subtraction. We will add 7 to both sides of the inequality and subtract 32 from both sides, resulting in 3b – 39 ≤ 0.
Step 3: Solve the Inequality
Now that the variable is on one side of the inequality sign, we can solve the inequality. To do this, we will divide both sides of the inequality by 3, resulting in b ≤ -13. This is the solution to the inequality. The solution tells us that any value of b that is less than or equal to -13 will make the inequality true.
Step 4: Check the Solution
Once we have our solution, it is always important to check it to make sure it is correct. To do this, we will substitute -13 into the original inequality and see if it makes the inequality true. If it does, then our solution is correct. When we substitute -13 into the original inequality, we get 3(-13) -7 + 32 = 0, which is true. Therefore, our solution is correct.
Solving inequalities can be a difficult process but with practice, it can become easier. In this article, we discussed how to solve the inequality 3b-7 32. We started by simplifying the expression, then isolated the variable and solved the inequality. Finally, we checked our solution to make sure it was correct. With these steps in mind, you will be able to solve any inequality.
