Solving and Literal Equations

Solve for x:

• x = yb - v
• x = by - v
• x = by + v

What is the first step (after setting up your workspace) in solving this equation:
5x + 7 = 12

• Divide by 5
• Subtract 5
• Multiply by 7
• Subtract 7

Solve:
y = mx + b , for b

• y - mx = b
• y + mx = b
• ^y/_mx = b
• y + mx = -b

Solve the Equation:
^{1/4 - 1/2r = -3/4r}

• r = 1
• r = -1
• r = 0
• r = 10

Simplify each equation. Tell whether the equation has one solution, no solution, or infinitely many solutions.
3x - 8 = 3(x - 4) + 1

• one solution
• no solutions
• infinitely many solutions

Simplify each equation. Tell whether the equation has one solution, no solution, or infinitely many solutions.
3x - 7 = 3(x - 3) + 2

• one solution
• no solutions
• infinitely many solutions

Simplify each equation. Tell whether the equation has one solution, no solution, or infinitely many solutions.
5x + 6 = 6 + 3x

• one solution
• no solutions
• infinitely many solutions

Find the Error
What error did the student make when solving the equation:
1/5x + 6 = 3/5x + 5
1x + 6 = 3x + 5
-2x + 6 = 5
-2x = -1
x = 1/2

• The student found an incorrect common denominator
• The student did not multiply all terms by the common denominator
• The student did not use opposite operations appropriately
• The student did not correctly eliminate the variable from one side of the equation

 $A=\frac{bh}{2}$ 

Solve for b

•  $b=2A-h$  

•  $b=\frac{2A}{h}$  

•  $b=\frac{Ah}{2}$  

•  $b=\frac{A-2}{h}$  

S = 3F - 24  Solve for F

• F = (S + 24)/3
• F = S/3 + 24
• F = 3S + 24
• F = 3(S + 24)