Is This a Solution?

Is This a Solution? Sometimes they’ll give you an equation and a number and ask if that number is a solution to the equation. There are 2 ways to solve problems like this.

The Hard Way The hard way to answer the question is to solve the equation and see if the answer you get is the number they gave you. That sounds like a lot of work!

Bird’s nesting The easy way to answer the question is to bird’s nest the number. Bird’s nesting may sound silly but it will save you a world of hurt when it comes to sign mistakes.

Is – 3 a solution to 2x2 – 4x = 30? I’m going to rewrite the equation, but every time I get to a letter, I’m going to insert an open ( ) instead - the proverbial bird’s nest. 2( )2 – 4( ) = 30

See how the ( ) keeps everything straight! Let’s meet our little feathered friend! x = – 3 is the proposed solution Let’s fly him into his nest 2(– 3 )2 – 4(– 3 ) = 8 2( 9 ) + 12 = 8 18 + 12 = 30 30 = 30 It is a solution! See how the ( ) keeps everything straight!

Testing Solutions You can do it the hard way by solving the problem. You can do it the easy way by bird’s nesting! Replace all the letters with ( ) Fly the ‘bird’ into his ‘nest’ Follow the order of operations and the rules of signed numbers. If you get an identity – the same number on each side of the equal sign – it is a solution!