# Solving Equations with variables on both sides- YES!

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Solving Equations with variables on both sides- YES!
Chapter 2 Section 4 Solving Equations with variables on both sides- YES!

Remember our goal… When we solve equations we want to isolate the variable to discover its value. We want to find out how much the variable equals. Solution of the Equation: the value of the variable that makes the equation true

Also, remember our properties of equality…
Addition What you add to one side, you must also…? Multiplication If you multiply one side of the equation by a number, you must…?

So what looks different with this one?
Work backwards- the opposite direction of the order of operations. What’s the additive inverse of -21? 21 Additive identity! Now, we should multiply both sides by which number? In other words: what is the multiplicative inverse of 2? Now check your work and see if it checks out!!!

Two new types of solutions
Identity When the equation is always true x=x; or 5=5; or 7=6+1 No Solution When the equation is never true for any value 2 = 3; or -1 = 1

What identity looks like…
Distribute! Try to get your variables on the same side. Use your additive inverse as you work backwards. 0 is the additive identity, so we have 10 on both sides. They’re the same no matter what, hence identity!

What no solution looks like…
Combine like terms! Try to get your variables on the same side. Use your additive inverse of 6m, -6m. 0 is the additive identity! These can never be equal, hence no solution!