1. Classify the equation 7x+3=7x−4 as having one solution, no solution, or infinitely many solutions.
2. Classify the equation 4x+2=4x+2 as having one solution, no solution, or infinitely many solutions.
3. Classify the equation 5(10x+6)=50x−4 as having one solution, no solution, or infinitely many solutions.
4. Think About the Process
a. Which operations can be used to find the solution to 17x+163x−12=18(10x+17)?
A. Addition and multiplication
B. Addition, multiplication, and division
C. Subtraction and multiplication
D. Addition, subtraction, multiplication, and division
E. Subtraction, multiplication, and division
b. Solve 17x+163x−12=18(10x+17).
A. x=▪
B. The equation has infinitely many solutions.
C. The equation has no solution.
5. Which answer shows the correct solution for 6x+19x−4=5(5x+4)?
A. x=▪
B. The equation has infinitely many solutions.
C. The equation has no solution.
6. Which answer shows the correct solution for 10x+22x−5=8(4x+7)?
A. x=▪
B. The equation has infinitely many solutions.
C. The equation has no solution.
7. Which answer shows the correct solution for 4(2x+4)=10x+15−2x+1?
A. x=▪
B. The equation has infinitely many solutions.
C. The equation has no solutions.
8. Solve 4(2x+3)=16x+3−8x+9.
A. x=▪
B. The equation has infinitely many solutions.
C. The equation has no solution.
9. Which answer shows the correct solution for 3x+x+2=8x−4x+2?
A. x=▪
B. The equation has infinitely many solutions.
C. The equation has no solution.
10. Think About the Process
a. What is a possible first step in solving 0.4(3x+18)=1.2(x+6)?
A. Multiply each side by 10.
B. Subtract 10 from each side.
C. Add 10 to each side.
D. Divide each side by 10.
b. Solve 0.4(3x+18)=1.2(x+6).
A. x=▪
B. The equation has infinitely many solutions.
C. The equation has no solution.
11.
a. Writing Classify the equation 49x+33=49x+38 as having one solution, no solution, or infinitely many solutions.
b. Write an equation that has one solution, an equation that has no solution, and an equation that has infinitely many solutions.