Solving The Inequality 3B-7<32

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Introduction

In mathematics, an inequality is a statement that compares two values or expressions using an inequality symbol. It is used to show that one value is less than or greater than the other. Solving an inequality involves finding the values of the variable that make the inequality true. In this article, we will discuss how to solve the inequality 3b-7<32.

Understanding the Inequality

The inequality 3b-7<32 means that 3 times b minus 7 is less than 32. To solve this inequality, we need to find the values of b that make this statement true. We can do this by manipulating the inequality to isolate b.

Isolating b

To isolate b, we need to get rid of the constant terms first. We can do this by adding 7 to both sides of the inequality, like this: 3b-7+7<32+7 Simplifying this, we get: 3b<39

Dividing by 3

To isolate b completely, we need to get rid of the coefficient of b, which is 3. We can do this by dividing both sides of the inequality by 3, like this: 3b/3<39/3 Simplifying this, we get: b<13

Solution

Therefore, the solution to the inequality 3b-7<32 is b<13. This means that any value of b less than 13 will make the inequality true.

Graphical Representation

We can also represent the solution to the inequality graphically. To do this, we can draw a number line and shade the region that represents the values of b that make the inequality true. In this case, we shade the line to the left of 13, since any value of b less than 13 will satisfy the inequality.

Graphical Representation of Inequality

Conclusion

Solving inequalities is an important skill in mathematics. In this article, we discussed how to solve the inequality 3b-7<32. We showed that the solution to the inequality is b<13, and we also represented this solution graphically. Remember that when solving an inequality, we need to manipulate the inequality to isolate the variable and find the values that make the inequality true.