Question

1. use the equation $4.9x - 1.9 = 27.5$.

a. make sense and persevere what two properties of equality do you need to use to solve the equation?
b. the solution is $x = \square$.

Explanation:

Part a

To solve the equation \(4.9x - 1.9 = 27.5\), we first need to isolate the term with \(x\). The addition property of equality (adding 1.9 to both sides) is used to eliminate the \(-1.9\) on the left. Then, the division property of equality (dividing both sides by 4.9) is used to solve for \(x\). So the two properties are the addition property of equality and the division property of equality.

Step1: Add 1.9 to both sides

To isolate the term with \(x\), we use the addition property of equality. Add 1.9 to both sides of the equation \(4.9x - 1.9 = 27.5\):
\[
4.9x - 1.9 + 1.9 = 27.5 + 1.9
\]
Simplifying both sides gives:
\[
4.9x = 29.4
\]

Step2: Divide by 4.9

Now, use the division property of equality. Divide both sides of the equation \(4.9x = 29.4\) by 4.9:
\[
x=\frac{29.4}{4.9}
\]
Calculating the right - hand side, we know that \(29.4\div4.9 = 6\).

Answer:

Addition property of equality and division property of equality

Part b