Question

8 chloe is solving the equation $x^2 + 5x = 3x + 3$. her first step is shown below. given: $x^2 + 5x = 3x + 3$ step 1: $x^2 + 2x - 3 = 0$ which property justifies this step? (1) the zero product property (2) the commutative property (3) the distributive property (4) the subtraction property of equality 9 which function represents the graph of $w(x) = |x|$ shifted 2 units to the right? (1) $g(x) = |x + 2|$ (2) $h(x) = |x - 2|$ (3) $q(x) = |x| + 2$ (4) $r(x) = |x| - 2$

Explanation:

(Problem 8):

Step1: Identify operation used

Chloe subtracted $3x + 3$ from both sides:
$x^2 + 5x - (3x + 3) = 3x + 3 - (3x + 3)$

Step2: Simplify to verify

$x^2 + 5x - 3x - 3 = 0$ which simplifies to $x^2 + 2x - 3 = 0$. This uses the rule that subtracting the same value from both sides of an equation preserves equality.

(Problem 9):

Step1: Recall horizontal shift rule

For a function $f(x)$, shifting right by $a$ units gives $f(x-a)$.

Step2: Apply rule to $w(x)=|x|$

Shift right 2 units: $w(x-2)=|x-2|$.

Answer:

1. (4) the subtraction property of equality
2. (2) $h(x) = |x - 2|$