Respuesta :
Answer and Explanation:
Given the below equation;
[tex]8x+11=3(7-4x)+15x[/tex]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;
[tex]8x+11=21-12x+15x[/tex]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;
[tex]8x+11=21+3x[/tex]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;
[tex]\begin{gathered} 8x-3x+11=21+3x-3x \\ 5x+11=21 \end{gathered}[/tex]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;
[tex]\begin{gathered} 5x+11-11=21-11 \\ 5x=10 \end{gathered}[/tex]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;
[tex]\begin{gathered} \frac{5x}{5}=\frac{10}{5} \\ x=2 \end{gathered}[/tex]