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

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

Note:

Trying to solve an equation with variables on both sides of the equal sign? Figure out how to get those variables together and find the answer with this tutorial!

Keywords:

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

Background Tutorials

  • 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!

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

      What's the Subtraction 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 subtraction property of equality, and it lets you subtract the same number from both sides of an equation. Watch the video to see it in action!

  • Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

      • How Do You Figure Out the Sign of a Product or Quotient?How Do You Figure Out the Sign of a Product or Quotient?

      How Do You Figure Out the Sign of a Product or Quotient?

      Multiplying and dividing numbers takes a good amount of thinking, and it's easy to make a mistake. But you can make sure that you're on the right track if you check whether the answer should be positive or negative. In this tutorial you'll see exactly how to tell if your answer will be positive or negative, even if you don't know the exact value of the answer. That way you'll always be able to check your answers!

  • Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

      • What are Like Terms?What are Like Terms?

      What are Like Terms?

      Combining like terms together is a key part of simplifying mathematical expressions, so check out this tutorial to see how you can easily pick out like terms from an expression

  • 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

  • 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).

  • Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

  • Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.