Question

study guide for math 8 final
questions 1 - 3: fill in the missing information for the equation 3x + 1 + 7 = 8x + 3

1. reason:

3x + 1 + 7 = 8x + 3

1. evidence:

Explanation:

Step1: Simplify left - hand side

First, we simplify the left - hand side of the equation \(3x + 1+7=8x + 3\). We combine the constant terms \(1\) and \(7\). According to the addition of real numbers, \(1 + 7=8\). So the left - hand side becomes \(3x+8\). The equation is now \(3x + 8=8x+3\).

Step2: Subtract \(3x\) from both sides

To get all the \(x\) terms on one side, we subtract \(3x\) from both sides of the equation \(3x + 8=8x + 3\). Using the subtraction property of equality (if \(a = b\), then \(a - c=b - c\)), we have \((3x + 8)-3x=(8x + 3)-3x\). Simplifying both sides, the left - hand side is \(8\) and the right - hand side is \(5x+3\). So we get \(8 = 5x+3\).

Step3: Subtract 3 from both sides

Next, we subtract \(3\) from both sides of the equation \(8 = 5x+3\). Using the subtraction property of equality, \((8)-3=(5x + 3)-3\). Simplifying, we get \(5 = 5x\).

Step4: Divide both sides by 5

Then, we divide both sides of the equation \(5 = 5x\) by \(5\). Using the division property of equality (if \(a = b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\)), we have \(\frac{5}{5}=\frac{5x}{5}\). Simplifying, we get \(x = 1\).

Answer:

The solution to the equation \(3x + 1+7 = 8x+3\) is \(x = 1\)