Practice identifying solutions to linear equations

This equation has one solution. 5(x - 1) + 3x = 7(x + 1) What is the solution?

x = 12

Complete the equation so it has infinitely many solutions 4x + 7 = 4(x + 3) - ?

5

Examine the equation. 4(x - 3) = 4x - 12 Which of the following is true? (Check all that apply.) a. It is a true statement. b. Any input will result in an equivalent equation c. It is equivalent to an equation of the form a = a d. It has no solution. e. Only one input will result in a true statement.

a. It is a true statement. b. Any input will result in an equivalent equation. c. It is equivalent to an equation of the form a = a.

which equation has infinitely many solutions? a. 5 (2x + 4) = 10x -12 b. 5 (2x + 4) =10(x + 2) c. 5 (2x + 4) =12x d. 5 (2x + 10) =20(x+1)

b

Explain how to create an equation with infinitely many solutions

With any statement in the form a = a. Then add the same variable term to both sides, and add the same constant term to both sides. Combine like terms on each side

Solve the equation . -3x + 9 = - 3(2x + 3) + 3(x - 4) + 1 How many solutions does this equation have? a. one solution b. two solutions c. infinitely many solutions d. no solution

d.

Examine the solution to the equation. -6 (x + 5) + 3 = -2 ( x + 4) -4 x -6x - 30 + 3 = -2x - 8 - 4x -6x - 27 = - 6x -8 -27 = -8 Which statements accurately describe this equation? check all that apply a. this equation has one solution. b. this equation has no solution. c. this equation has infinitely many solutions d. any input value for variable will generate a true equation e. any input value for variable will generate a false equation

b. this equation has no solution. e. any input value for variable will generate a false equation

Adam solved this equation and identified the number of solutions. 24x - 22 = 4(6x - 1) 24x - 22 = 24x - 4 24x = 24x + 18 0 = 18 The equation has infinitely many solutions. When Adam verified his answer, it didn't work. What was his mistake? a. He used the distributive property incorrectly in the first step b. He used the addition property of equality incorrectly in the second step c. he should of found that the equation has one solution of x=18 d. he should have found that there are no solutions because the statement is false

d

Examine the equation .-2(-x + 9) = 2(x - 9) 2x - 18 = 2x - 18 This equation has: A. one solution B. infinitely many solutions C. no solution

B. infinitely many solutions

Which linear equations have one solution? check all that apply a. 5x - 1 = 3(x +11) b. 4(x - 2) + 4x = 8(x - 9) c. 4(x - 6) + 4 = 2(x - 3) d. 2(x-4) = 5(x-3) + 3 e. 2(x - 1)+3x=5(x-2)+3

a. c d