Solving equations with fractions

Task goals

• Solve a one-step equation where the variable is divided by a number, such as x/3 = 7.
• Solve a two-step equation involving a fraction, such as x/4 + 3 = 8 or 2x/3 = 8.
• Solve an equation where a binomial expression is divided by a number, such as (x + 1)/2 = 5.
• Solve an equation with the unknown in the denominator, such as 5/(x + 2) = 1.
• Solve an equation with two fractional terms containing the variable, by finding a common denominator, such as x/2 + x/4 = 6.
• Solve an equation where a fraction is set equal to another fraction, by cross-multiplying, such as (x + 1)/2 = (x - 3)/5.
• Solve a worded problem that translates to a fractional equation, and identify or explain an error in a given (possibly incorrect) solution to a fractional equation.
• Explain why multiplying every term by the lowest common denominator clears the fractions from an equation.