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Chapter 5: Problem 67

Write an inequality to represent the statement. \(y\) is at least -2 .

Short Answer

Expert verified
y \geq -2

Step by step solution

01

Understand the Statement

The statement says that the variable y is at least -2. This means that y is either greater than or equal to -2.
02

Write the Inequality

To represent that y is at least -2, we use the inequality symbol for 'greater than or equal to' (鈮�). Therefore, the inequality can be written as: \[ y \geq -2 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

algebraic expressions
Algebraic expressions are mathematical phrases that include numbers, variables, and operators. In algebra, variables are symbols that represent unknown values and can vary. For example, in the expression \(3x + 2\), \(3x\) and \(2\) are the terms, where \(x\) is the variable.
An important part of working with algebraic expressions is simplifying them by combining like terms and using operations like addition, subtraction, multiplication, and division. Understanding how to manipulate these expressions is critical for solving equations and inequalities.
inequality symbols
Inequality symbols are used to compare two values or expressions. The most common inequality symbols are:
  • \( > \): greater than
  • \( < \): less than
  • \( \geq \): greater than or equal to
  • \( \leq \): less than or equal to

These symbols help us express relationships where the values are not necessarily equal. For instance, in the statement 'y is at least -2', the term 'at least' indicates that \(y\) can be equal to -2 or any value greater than -2. This leads us to write the inequality as \(y \geq -2\). Using the correct inequality symbol ensures that the relationship is accurately represented.
solving inequalities
Solving inequalities involves finding the range of values that make the inequality true. The process is similar to solving equations, but there are a few key differences to keep in mind. For example, when multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality symbol.
Here鈥檚 a step-by-step approach for solving a simple inequality:
  • Isolate the variable on one side of the inequality, using addition or subtraction.
  • Simplify the expression, if necessary.
  • If you need to multiply or divide to isolate the variable, remember to flip the inequality sign if you are dealing with a negative number.

Consider the example: Solve \(-3x < 9\). You would divide both sides by \(-3\), and since you are dividing by a negative number, you flip the inequality sign. This gives you \(x > -3\). It鈥檚 important to be careful with these steps to ensure that your solution is correct.

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Most popular questions from this chapter

The average weekly salary of two employees is \(\$ 1350\). One makes \(\$ 300\) more than the other. Find their salaries

An investment grows exponentially under continuous compounding. After 2 yr, the amount in the account is \$7328.70. After 5 yr, the amount in the account is \$8774.10. Use the model \(A(t)=P e^{r t}\) to a. Find the interest rate \(r\). Round to the nearest percent. b. Find the original principal \(P\). Round to the nearest dollar. c. Determine the amount of time required for the account to reach a value of \(\$ 15,000 .\) Round to the nearest year.

Solve the system. $$ \begin{array}{l} \log _{2} x+3 \log _{2} y=6 \\ \log _{2} x-\log _{2} y=2 \end{array} $$

a. Sketch the lines defined by \(y=2 x\) and \(y=-\frac{1}{2} x+5\) b. Find the area of the triangle bounded by the lines in part (a) and the \(x\) -axis.

Use a graphing utility to approximate the solution(s) to the system of equations. Round the coordinates to 3 decimal places. $$ \begin{array}{l} x^{2}+y^{2}=40 \\ y=-x^{2}+8.5 \end{array} $$
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