Create an expression that you could solve with two different numbers below, right the expression, and solve it with two different numbers for the variable, remembering the order of operations
Let's construct a simple algebraic expression with one variable, x, that we can solve using two different values for x.
Expression: \( 2x + 3(4 - x) \)
Remember the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), commonly abbreviated as PEMDAS.
Now, let's solve this expression for two different values of x. For instance, let's use x = 2 for the first case and x = 5 for the second case.
1. When \( x = 2 \):
\( 2x + 3(4 - x) \)
\( = 2(2) + 3(4 - 2) \) Apply the values inside the parentheses first.
\( = 4 + 3(2) \) Multiply.
\( = 4 + 6 \) Addition.
\( = 10 \)
So, when \( x = 2 \), the expression evaluates to 10.
2. When \( x = 5 \):
\( 2x + 3(4 - x) \)
\( = 2(5) + 3(4 - 5) \) Apply the values inside the parentheses first.
\( = 10 + 3(-1) \) Multiply.
\( = 10 - 3 \) Perform the addition and subtraction.
\( = 7 \)
So, when \( x = 5 \), the expression evaluates to 7.
Hence for two different values of x, we obtained two results:
- When \( x = 2 \), the expression equals 10.
- When \( x = 5 \), the expression equals 7.