Solving Linear Equations: Distributive Property

zero

How many solutions exist for the given equation solution? 3x + 13 = 3(x + 6) + 1

one

How many solutions exist for the given equation? 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)

one

How many solutions exist for the given equation? 1/2(x + 12) = 4x - 1

one

How many solutions exist for the given equation? 3(x - 2) = 22 - x

no solution

How many solutions exist for the given equation? 5 + 2(3 + 2x) = x + 3(x + 1)

infinitely many

How many solutions exist for the given equations? 12x + 1 = 3(4x + 1) -2

The equation has infinite solutions.

Jillana begins to solve a linear equation that results in a variable expression set equal to the same variable expression. Which is the best interpretation of this solution?

0

Karissa begins to solve the equation 1/2x (x - 14) + 11 = 1/2x - (x - 4). Her work is correct and is shown below. When she subtracts 4 from both sides, 1/2x = -1/2x results. What is the value of x?

The equation has one solution: x = 0.

Kate begins solving the equation 2/3(6x - 3) = 1/2(6x - 4). Her work is correct and is shown below. When she adds 2 to both sides, the equation 4x = 3x results. Which is the best interpretation of this equation?

The equation has no solution.

Lily begins solving the equation 4(x - 1) - x = 3(x + 5) - 11. Her work is shown below. How can her partial solution be interpreted?

n = 11

Solve for n. n + 1 = 4(n - 8)

x = 4

Solve for x. 5(x - 10) = 30 - 15x

x = -8

Solve for x. 6(x - 1) = 9(x + 2)

x = 2

Solve for x. 9(x + 1) = 25 + x

4

What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x -2)?

2

What is the value of x in the equatjon 2.5(6x - 4) = 10 + 4(1.5 + 0.5x)?

2

What us the value of n in the equation 1/2(n - 4) - 3 = 3 - (2n + 3)? n =

4

What us the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?