To solve the equation [tex]\(-3 + 4x = 9\)[/tex], Verona needs to isolate the variable term [tex]\(4x\)[/tex]. Here's a step-by-step approach on how to achieve that:
1. Understand the goal: Isolate [tex]\(4x\)[/tex] on one side of the equation.
2. Identify the constant term: The constant term on the left side of the equation is [tex]\(-3\)[/tex].
3. Eliminate the constant term: To move [tex]\(-3\)[/tex] to the other side of the equation, we need to add its opposite. The opposite of [tex]\(-3\)[/tex] is [tex]\(3\)[/tex].
4. Apply the addition: We add [tex]\(3\)[/tex] to both sides of the equation to maintain the balance.
[tex]\[
-3 + 3 + 4x = 9 + 3
\][/tex]
5. Simplify the new equation: The left side simplifies as follows:
[tex]\[
(-3 + 3) + 4x = 12
\][/tex]
Since [tex]\(-3 + 3 = 0\)[/tex], we get:
[tex]\[
4x = 12
\][/tex]
Thus, the number that Verona should add to both sides of the equation in order to isolate the variable term using the addition property of equality is [tex]\(3\)[/tex].
