Math Problem Statement

Solve for x in the given equations.

Solution

Let's solve the equations from the images you uploaded. I will first extract and solve the equations from both images.

Image 1: Solving for xx

  1. xy=wx - y = w

    • Solving for xx: x=y+wx = y + w
  2. xvw=y\frac{x}{v - w} = y

    • Solving for xx: x=y(vw)x = y(v - w)
  3. x+6y=3vx + 6y = 3v

    • Solving for xx: x=3v6yx = 3v - 6y
  4. v9x=wy\frac{v}{9x} = \frac{w}{y}

    • Solving for xx: x=9vywx = \frac{9vy}{w}
  5. x+v=wx + v = w

    • Solving for xx: x=wvx = w - v
  6. vxw=2vx - w = 2

    • Solving for xx: x=w+2vx = \frac{w + 2}{v}
  7. 3v+x=w3v + x = w

    • Solving for xx: x=w3vx = w - 3v
  8. 6w+vx=y6w + vx = y

    • Solving for xx: x=y6wvx = \frac{y - 6w}{v}

Image 2: Solving for xx

  1. a(x+b)=ca(x + b) = c

    • Solving for xx: x=cabx = \frac{c}{a} - b
  2. 2(x+a)=b2(x + a) = b

    • Solving for xx: x=b2ax = \frac{b}{2} - a
  3. a(x2)=ba(x - 2) = b

    • Solving for xx: x=ba+2x = \frac{b}{a} + 2
  4. c(9+x)=6c(9 + x) = 6

    • Solving for xx: x=6c9x = \frac{6}{c} - 9

Would you like more details on any specific steps or solutions?

Related Questions:

  1. How can I simplify more complex equations with multiple variables?
  2. What happens when there are no real solutions to an equation?
  3. Can you solve equations involving exponents for xx?
  4. How do you isolate xx in an equation with a fraction?
  5. What if xx appears in the denominator? How can I solve for it?

Tip: Always try to move all terms involving xx to one side of the equation and constants to the other to simplify the solving process!

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Math Problem Analysis

Mathematical Concepts

Algebra
Solving for variables
Linear equations

Formulas

x = y + w
x = y(v - w)
x = 3v - 6y
x = 9vy/w
x = w - v
x = (w + 2)/v
x = w - 3v
x = (y - 6w)/v
x = (c/a) - b
x = (b/2) - a
x = (b/a) + 2
x = (6/c) - 9

Theorems

Algebraic manipulation
Cross-multiplication

Suitable Grade Level

Grades 8-10