Solving Linear Equations: Distributive Property

Solve the equation: 3/5(x-10) = 18 - 4x - 1

1. 3/5 2. 18 and -1 3. subtracting 17 4. subtracting 3/5x 5. -5/23

Which linear equations have an infinite number of solutions? Check all that apply. A. (x - 3/7) = 2/3 (3/2x - 9/14) B. 8(x + 2) = 5x - 14 C. 12.3x - 18 = 3(-6 + 4.1x) D. 1/2(6x + 10) = 7(3/7x - 2) E. 4.2x - 3.5 = 2.1 (5x + 8)

A. (x - 3/7) = 2/3 (3/2x - 9/14), and C. 12.3x - 18 = 3(-6 + 4.1x)

solve the equation. 4-2(x+7) = 3(x+5)

add 10 subtract 3x divide -5 x = -5

Sort each equation according to whether it has one solution, infinitely many solutions, or no solution.

one solution: -2(x -3) = 2x -6 and 4(x + 1) = 3x + 4 infinitely many solutions: -3(x - 4) = -3x + 12 no solution: 5(x - 2) = 5x - 7 and 6(x + 5) = 6x + 11

Solve this linear equation for p: 2.6(5.5p - 12.4) = 127.92 1. Distributive property: 2. Addition property of equality: 3. Division property of equality: 4. Solution:

14.3p - 32.24 = 127.92 14.3p - 32.24 + 32.24 = 127.92 + 32.24 14.3p = 160.16 p = 11.2

Micah solves a linear equation and concludes that x = 0 is the solution. His work is shown below. 5/6(1 - 3x) = 4(-5x/8 + 2) 5/6 - 5x/2 = -5x/2 + 8 +5x/2 +5x/2 0 = x Which statement is true about Micah's solution? 1. Micah's solution is wrong. There are no values of x that make the statement true. 2. Micah's solution is correct, and the value of x that makes the statement true is 0. 3. Micah should have divided by 5/2. 4. Micah should have subtracted 5/2.

answer: 1.