If x = -3, what is the value of the expression 2x^2 - 4(x - 1) + |x - 5|? — ACT

If $x = -3$ , what is the value of the expression $2x^2 - 4(x - 1) + |x - 5|$ ?

The correct answer is 42. Following the order of operations, we first substitute

x = -3

to get

2(-3)^2 - 4(-3 - 1) + |-3 - 5|

. First, evaluate grouping terms:

(-3 - 1) = -4

and

|-3 - 5| = |-8| = 8

. Next, evaluate exponents:

(-3)^2 = 9

. Then, perform multiplications:

2 \times 9 = 18

and

-4 \times -4 = 16

. Finally, perform addition from left to right:

18 + 16 + 8 = 42

Substitute

x = -3

into the given expression.

2(-3)^2 - 4((-3) - 1) + |(-3) - 5|

This sets up the expression for numerical evaluation.

Evaluate the terms inside the parentheses and absolute value bars.

Parentheses:

-3 - 1 = -4

; Absolute value:

|-3 - 5| = |-8| = 8

According to the order of operations (PEMDAS), operations inside grouping symbols must be performed first.

Evaluate the exponential term.

(-3)^2 = 9

Exponents must be calculated after grouping symbols and before multiplication.

Perform the multiplications from left to right.

2(9) = 18

and

-4(-4) = 16

Multiplication takes precedence over addition and subtraction.

Add the remaining values.

18 + 16 + 8 = 42

Addition and subtraction are performed from left to right to get the final result.

Evaluating algebraic expressions containing variables, exponents, parentheses, and absolute values using the standard order of operations (PEMDAS).

Estimated Time:1m 15s

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