Question

1. given the following equation solve for (y): (4y - 7 = x) 16) determine the proper reasoning for each step that is performed on the following equation. circle the correct reasoning on each step. (4 points) ((4x - 10)=2x + 4) original equation a) distribution b) subtracting the same term from both sides c) adding the same term to both sides d) dividing each side by the same number (4x=2x + 4) a) distribution b) subtracting the same term from both sides c) adding the same term to both sides d) dividing each side by the same number (10x-40 = 4) a) distribution b) subtracting the same term from both sides c) adding the same term to both sides d) dividing each side by the same number (10x = 44) a) distribution b) subtracting the same term from both sides c) adding the same term to both sides d) dividing each side by the same number (x = 4.4) a) distribution b) subtracting the same term from both sides c) adding the same term to both sides d) dividing each side by the same number

Explanation:

Step1: Expand the left - hand side

We start with the equation \(5(2x - 8)=2x + 4\). Using the distributive property \(a(b - c)=ab - ac\), where \(a = 5\), \(b = 2x\) and \(c = 8\), we get \(10x-40 = 2x + 4\). So the reason for this step is distribution.

Step2: Isolate the variable terms

We want to get all the \(x\) - terms on one side. We subtract \(2x\) from both sides of the equation \(10x-40 = 2x + 4\). This gives \(10x-2x-40=2x - 2x + 4\), which simplifies to \(8x-40 = 4\). The reason for this step is subtracting the same term from both sides.

Step3: Isolate the variable term further

We add 40 to both sides of the equation \(8x-40 = 4\). So \(8x-40 + 40=4 + 40\), which simplifies to \(8x=44\). The reason for this step is adding the same term to both sides.

Step4: Solve for \(x\)

We divide both sides of the equation \(8x = 44\) by 8. So \(x=\frac{44}{8}=4.4\). The reason for this step is dividing each side by the same number.

Answer:

1. \(10x-40 = 2x + 4\): a) distribution
2. \(8x-40 = 4\): b) subtracting the same term from both sides
3. \(8x = 44\): c) adding the same term to both sides
4. \(x = 4.4\): d) dividing each side by the same number