Question

problems 2–3: anna wants to create another equivalent equation to ( 9x + 12 = 21 ). here is anna’s equation.
( 18x + 24 = 42 )

1. is anna’s equation equivalent to ( 9x + 12 = 21 )? circle one.

yes no maybe

1. explain how anna determined her equivalent equation to ( 9x + 12 = 21 ).

Explanation:

Problem 2

Step 1: Recall the definition of equivalent equations

Equivalent equations have the same solution(s). We can check by solving both equations or by seeing if one can be transformed into the other using properties of equality.

Step 2: Analyze the transformation from \(9x + 12 = 21\) to \(18x + 24 = 42\)

Notice that if we multiply each term in \(9x + 12 = 21\) by 2:

• Multiply \(9x\) by 2: \(9x\times2 = 18x\)
• Multiply \(12\) by 2: \(12\times2 = 24\)
• Multiply \(21\) by 2: \(21\times2 = 42\)

So, \(2\times(9x + 12)=2\times21\) simplifies to \(18x + 24 = 42\) (using the distributive property \(a(b + c)=ab+ac\) with \(a = 2\), \(b = 9x\), \(c = 12\)).

Since we multiplied both sides of the original equation by the same non - zero number (2), the two equations are equivalent (they will have the same solution for \(x\)).

To determine her equivalent equation, Anna used the multiplication property of equality. The multiplication property of equality states that if we multiply both sides of an equation by the same non - zero number, the resulting equation is equivalent to the original equation. In the equation \(9x + 12 = 21\), Anna multiplied each term on the left - hand side (\(9x\) and \(12\)) and the right - hand side (21) by 2. When we multiply \(9x\) by 2, we get \(18x\); multiplying 12 by 2 gives 24; and multiplying 21 by 2 gives 42. So, she transformed \(9x + 12 = 21\) into \(18x + 24 = 42\) by multiplying both sides of the original equation by 2.

Answer:

Yes

Problem 3