Question

Justify each step of the solution by stating the name of the property that was used to get each step.given: 8x + 11 = 3(7-4x)+15xstep1: 8x+11=21-12x+15xstep2: 8x+11=21+3xstep3: 5x+11=21step 4: 5x=10step5: x = 2

Answer 1

Answer and Explanation:

Given the below equation;

`8x+11=3(7-4x)+15x`

Each of the properties that were used to arrive at each of the steps is as stated below;

Step 1: Distributive Property of Multiplication

To solve the given equation, the 1st step is to clear the parentheses using the distributive property of multiplication which involves using 3 to multiply through the terms in the parentheses, so we'll have;

`8x+11=21-12x+15x`

Step 2: Addition Property

The simplify Step 1 further we need to add like terms( -12x + 15x = 3x) in the right-hand side of the equation, so we'll have;

`8x+11=21+3x`

Step 3: Subtraction Property of Equality

To simplify Step 2 further, we have to subtract 3x from both sides of the equation, so we'll have;

`\begin{gathered} 8x-3x+11=21+3x-3x \\ 5x+11=21 \end{gathered}`

Step 4: Subtraction Property of Equality

To simplify Step 3 further, we have to subtract 11 from both sides of the equation, so we'll have;

`\begin{gathered} 5x+11-11=21-11 \\ 5x=10 \end{gathered}`

Step 5: Division Property of Equality

To simplify Step 4 further, we have to divide both sides of the equation by 5, so we'll have;

`\begin{gathered} (5x)/(5)=(10)/(5) \\ x=2 \end{gathered}`