From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
What's the difference between an expression and an equation?
1: An expression doesn't have = signs, while an equation must.
2: An expression represents a quantity, while an equation is a claim that two such quantities are equal. An expression is part of an equation. You wouldn't say that your foot and your leg are the same thing, would you? If so, we apologize. You might wanna get that checked out.
What's a solution to an equation?
A solution is a value that, when substituted for the variable, makes the equation true.
Is a solution to the equation
Yep. The left-hand side evaluates to 3 – 3 = 0, while the right-hand side evaluates to .
Is x = 0.5 a solution to the equation
No. The left-hand side evaluates to 2(0.5) + 0.5 = 1.5, while the right-hand side evaluates to .
Is z = 4 a solution to the equation
Nope. The left side comes out to 16 – 8 – 1 = 7, but the right sides gives us 3(4) – 8 = 4.
Is y = 2 a solution to the equation
Yes indeedy. Plug in y = 2 on the left side to get 4 – 1 = 3, which matches up perfectly with 1 + 2 = 3 on the right side.
Is y = -2 a solution to the equation
It totally is. The left-hand side evaluates to (-2)2 – 1 = 4 – 1 = 3, and the right-hand side evaluates to |-1| + 2 = 1 + 2 = 3.