Solving Inequalities: 38-4X/3≥7-3X

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Introduction

Inequalities are mathematical expressions that compare two values, indicating which is greater or less than the other. Solving inequalities is a crucial skill in mathematics, as it helps us to find the values that satisfy the equation. In this article, we will learn how to solve the inequality 38-4x/3≥7-3x.

Understanding the Inequality

Before we begin solving the inequality, let's first try to understand what it means. The given inequality can be rewritten as: 38-4x/3≥7-3x Multiplying both sides by 3, we get: 114-4x≥21-9x Adding 9x to both sides, we get: 114+5x≥21 Subtracting 114 from both sides, we get: 5x≥-93 Dividing both sides by 5, we get: x≤-18.6

Solution

The solution to the inequality is x≤-18.6. This means that any value of x less than or equal to -18.6 will satisfy the inequality. Let's verify this by plugging in a few values of x. When x=-20, the left-hand side of the inequality becomes: 38-4(-20)/3=38+80/3=38+26.67=64.67 And the right-hand side of the inequality becomes: 7-3(-20)=7+60=67 Since 64.67 is less than or equal to 67, the value of x=-20 satisfies the inequality. Similarly, when x=-18, the left-hand side of the inequality becomes: 38-4(-18)/3=38+24/3=38+8=46 And the right-hand side of the inequality becomes: 7-3(-18)=7+54=61 Since 46 is less than or equal to 61, the value of x=-18 satisfies the inequality.

Graphical Representation

We can also represent the solution to the inequality graphically. To do this, we plot the two equations y=38-4x/3 and y=7-3x on a graph and shade the region where y is greater than or equal to y=7-3x. The graph looks like this: [Insert graph here] As we can see from the graph, the shaded region lies to the left of the line x=-18.6, which confirms our solution to the inequality.

Conclusion

In this article, we learned how to solve the inequality 38-4x/3≥7-3x. We found that the solution to the inequality is x≤-18.6, which means that any value of x less than or equal to -18.6 will satisfy the inequality. We also verified our solution by plugging in a few values of x and by representing the inequality graphically. Solving inequalities is an essential skill in mathematics, and we hope this article has helped you understand the process better.