Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write the steps in solving
−
2
x
+
5
(
x
+
3
)
=
−
9
. Justify each step with an appropriate property.
first, get rid of all those line feeds, and write it so we can read it.
Sure! To solve the equation −2x + 5(x + 3) = −9, we need to simplify and isolate the variable x. Here are the steps:
Step 1: Distribute the 5 to the terms inside the parentheses:
-2x + 5(x) + 5(3) = -9
Property used: Distributive Property
Step 2: Multiply the values:
-2x + 5x + 15 = -9
Property used: Distributive Property
Step 3: Combine like terms on the left side of the equation:
(-2x + 5x) + 15 = -9
3x + 15 = -9
Property used: Commutative Property of Addition
Step 4: Move the constant term to the right side of the equation by subtracting 15 from both sides:
3x + 15 - 15 = -9 - 15
3x = -24
Property used: Subtraction Property of Equality
Step 5: Divide both sides of the equation by 3 to isolate x:
(3x)/3 = -24/3
x = -8
Property used: Division Property of Equality
So, the solution to the equation −2x + 5(x + 3) = −9 is x = -8.