Question

pre-algebra #10
evaluating algebraic expressions using integers
example 1: evaluate 8 + 2x if x = -3. we must substitute -3 every place an “x” appears in the expression.
8 + 2(-3)
8 + (-6) = 2
it is a good idea to use parentheses when substituting, especially when multiplication is indicated.
practice exercises: evaluate for the given value of the variable.
1.) 3 + 4x if x = -2
3 + 4( ) =
2.) -6 + 5x if x = -1
-6 + 5( ) =
3.) 6x + 4 if x = -1
4.) 8x + 5 if x = -2
5.) -2x + 3 if x = 2
6.) -2x + 5 if x = -2
7.) -6r + 8s if r = -2 and s = 4
answer to 2.) -11
example 2: evaluate 8 - 2x if x = -3
8 - 2x
= 8 + -2x
= 8 + -2(-3)
= 8 + 6
= 14
this time we have a “minus” sign between the two terms.
1.) change all subtraction to addition.
2.) then substitute.
practice exercises: evaluate for the given value of the variable. show all work!!
2 - 4x if x = -2
1.) 2 + -4x =
2 + -4( ) =
2.) 3x - 8 if x = -2

Explanation:

Step1: Substitute \( x = -2 \) into \( 3 + 4x \)

We replace \( x \) with \( -2 \) in the expression \( 3 + 4x \), so we get \( 3 + 4(-2) \).

Step2: Calculate the multiplication

First, calculate \( 4(-2) \). Multiplying 4 and -2 gives \( -8 \), so the expression becomes \( 3 + (-8) \).

Step3: Calculate the addition

Now, add 3 and -8. \( 3 + (-8) = 3 - 8 = -5 \).

Answer:

For the expression \( 3 + 4x \) when \( x = -2 \), the value is \(-5\).