How Do You Solve an Equation with Variables on Both Sides and Fractions?

How Do You Solve an Equation with Variables on Both Sides and Fractions?

Note:

Trying to solve an equation with variables and fractions on both sides of the equation? You can bet it involves finding a common denominator! To see what it takes, watch this tutorial.

Keywords:

  • problem
  • equation
  • solve
  • fractions
  • linear equation
  • variable on both sides
  • 1 variable
  • distributive property
  • multiplication property of equality
  • solve by subtraction
  • solve by division

Background Tutorials

  • Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

      • What is a Variable?What is a Variable?

      What is a Variable?

      You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

  • Apply the properties of operations to generate equivalent expressions.

  • Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

      • What's the Multiplication Property of Equality?What's the Multiplication Property of Equality?

      What's the Multiplication Property of Equality?

      Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the multiplication property of equality, and it lets you multiply both sides of an equation by the same number. Watch the video to see it in action!

  • Apply properties of operations as strategies to add and subtract rational numbers.

  • Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Further Exploration