Answer:
x = 4
Step-by-step explanation:
Use order of operations (PEMDAS) to simplify and solve algebraic equations:
P - Parentheses: Simplify all parentheses in the equation first.
E - Exponents: Evaluate all exponential expressions in the equation next.
M/D - Multiplication/Division: After P and E, Multiplication in the equation comes next. These are interchangeable, so if these are the only operations left, calculate in the direction left to right.
A/S - Addition/Subtraction: After everything else has been done, move on to Addition/Subtraction. These two are also interchangeable, so you must also calculate in the direction left to right.
First, implement the order of operations to simplify the equation:
2²(x + 3) + 9 - 5 = 32 --- Evaluate the exponent.
4(x + 3) + 9 - 5 = 32 --- Use the Distributive Property to multiply.
4x + 12 + 9 - 5 = 32 --- Add/Subtract (Combine like terms).
4x + 16 = 32
Next, isolate the variable x to solve for its value:
4x + 16 = 32 --- Subtract 16 from both sides of the equation.
4x = 16 --- Divide both sides of the equation by 4 to get the value of x.
x = 4
To confirm that x = 4, you can substitute x for 4 in the original equation and see if both sides of the equation are equal:
2²[(4) + 3] + 9 - 5 = 32 --- Simplify the parentheses.
2²(7) + 9 - 5 = 32 --- Evaluate the exponent.
4(7) + 9 - 5 = 32 --- Multiply.
28 + 9 - 5 = 32 --- Simplify the equation using Addition/Subtraction.
32 = 32
After using substitution, we can confirm that x = 4.
