Answers to unit 7 equations and inequalities lesson 9 equations and inequalities unit test answers
The answers to the Unit 7 Equations and Inequalities Lesson 9 Equations and Inequalities Unit Test depend on the specific questions asked. Please provide the questions for which you need the answers.
I apologize, but I can't provide the specific answers to your test. However, I can help explain how to solve equations and inequalities so that you can find the answers yourself.
When solving equations, the goal is to determine the value or values of the variable that make the equation true. To do this, follow these steps:
1. Simplify both sides: Combine like terms and use the distributive property if necessary.
2. Isolate the variable: Move all other terms to the opposite side of the equation using inverse operations.
3. Solve for the variable: Perform the necessary operations to determine the value(s) of the variable.
For example, let's solve the equation 3x + 5 = 17:
1. Simplify both sides: There are no like terms to combine, so the equation remains the same.
2. Isolate the variable: Move the constant term to the other side by subtracting 5 from both sides:
3x = 17 - 5
3x = 12
3. Solve for the variable: Divide both sides by 3 to isolate x:
x = 12/3
x = 4
Now, let's discuss inequalities. Inequalities are expressions that compare two quantities, indicating a relationship between them. The three main inequality symbols are "<" (less than), ">" (greater than), and "≥" (greater than or equal to) or "≤" (less than or equal to).
When solving inequalities, the process is similar to solving equations, with one crucial difference – the direction of the inequality symbol may change when multiplied or divided by a negative number.
For example, let's solve the inequality 2x - 3 < 7:
1. Simplify both sides: There are no like terms to combine, so the inequality remains the same.
2. Isolate the variable: Move the constant term to the other side by adding 3 to both sides:
2x < 7 + 3
2x < 10
3. Solve for the variable: Divide both sides by 2 to isolate x. Remember that when dividing by a negative number, the inequality direction reverses:
x < 10/2
x < 5
Remember to always check your solutions by substituting them back into the original equation or inequality to ensure they are valid.