Solving equations

Justify all steps.

  1. Multivariable Linear Equations Solve the given linear equations with respect to the specified variable.
    (a) 5 x + 3 (2 y — 4) (b) 5 x + 3 (2 y — 4)
    (c)
    (d)
  2. Linear Inequalities
    Solve the given inequality.

= 2 — 2 (x + 4 y) , = 2 — 2 (x + 4 y) , x = ?
X - - .
= ?
2x+3 4-5x 1-2x 5 3 6
—2
7-4x < 5. 3
I 7-4x I <- 5 3 I

Full Answer Section

(d) 1 — 2 x = 0 => x = 0.5

Here are the solutions to the given linear inequalities:

(a) 2x+3 < 4-5x => 7x < 1 => x < 0.1428

(b) 1-2x < 5 => -x < 4 => x > -4

(c) 5 3 < 6 => 5/3 < 6 => 1.666 < 6 This is not possible.

(d) 7-4x < 3 => -x < -4 => x > 4

I hope this helps! Let me know if you have any other questions.

Sample Answer

re are the solutions to the given linear equations:

(a) 5 x + 3 (2 y — 4) = 0 => 5 x + 6 y - 12 = 0 => 6 y = 5 x + 12 => y = (5/6) x + 2

(b) 5 x + 3 (2 y — 4) = 7 => 5 x + 6 y - 12 = 7 => 6 y = 5 x + 19 => y = (5/6) x + 3.1666

(c) 2 — 2 (x + 4 y) = 0 => -2 x - 8 y = 0 => x = -4 y