1. Use the algebra tiles to find the value of x when the expression 6x + 2 equals 4x + 10. Simplify your answer.
2. What is the value of n when 6n − 10 = 4n + 6?
3. Think About the Process You are given the equation, 34 − 7x = 15 + 12x.
a. What would you do first to find x?
b. What value of x makes the equation true?
4. Find the value of x when 6 − 4x = 6x − 8x + 2.
5. Solve the equation to find the value of x. 6 − 6x = 5x − 9x − 2
6. A town's population is 43,425. About 125 people move out of the town each month. Each month, 200 people on average move into town. A nearby town has a population of 45,000. It has no one moving in and an average of 150 people moving away every month. In about how many months will the populations of the towns be equal?
a. Write an equation that models the situation.
b. In about how many months will the population of the towns be equal?
7.
a. Writing Find the value of g when 5g + 9 equals 2g + 15.
b. Explain how you can check that the value you found for g is correct. If your check does not work, does that mean that your result is incorrect? Explain.
8. Consider the equation 2x + 18 = 29 + 9 + x.
a. Which of these descriptions matches the given situation?
A. Multiply a number by 18 and add 2. The result is the same as the sum of 29, 9, and the number.
B. Double a number and add 18. The result is the same as the product of 29, 9, and the number.
C. Double the sum of a number and add 18. The result is the same as the sum of 29, 9, and the number.
D. Double a number and add 18. The result is the same as the sum of 29, 9, and the number.
E. Double the sum of a number and add 18. The result is the same as the product of 29, 9, and the number.
F. Multiply a number by 18 and add 2. The result is the same as the product of 29, 9, and the number.
b. Describe a real-world situation that could be represented by the equation.
9. Reasoning To solve an equation in x, you simplify the equation so that it becomes easy to tell which value(s) of x make the equation true.
a. Simplify −6x + 13 + 7x = 6 + x + 7 until you have the equation in the form x = . Tell what value(s) of x make the equation true.
b. What can you conclude about the original equation?
10. cap solve , equals , 5 thirds , x plus , 1 third , x equals 13 , and 1 third , plus , 8 thirds , x .