Question

1. $-5.4 - 7.8x = -78.408$

Explanation:

Step1: Add 5.4 to both sides

To isolate the term with \( x \), we add 5.4 to both sides of the equation \(-5.4 - 7.8x = -78.408\). This gives us \(-7.8x = -78.408 + 5.4\).

Step2: Calculate the right - hand side

First, calculate \(-78.408+5.4\). We know that adding a positive number to a negative number is equivalent to subtracting the absolute values and taking the sign of the number with the larger absolute value. So, \(\vert - 78.408\vert=78.408\) and \(\vert5.4\vert = 5.4\). Then \(-78.408 + 5.4=- (78.408 - 5.4)=-73.008\). So the equation becomes \(-7.8x=-73.008\).

Step3: Solve for x

To solve for \( x \), we divide both sides of the equation \(-7.8x=-73.008\) by \(-7.8\). Using the formula \(x=\frac{-73.008}{-7.8}\), and since dividing two negative numbers gives a positive result, we calculate \(\frac{73.008}{7.8}\). \(73.008\div7.8 = 9.36\).

Answer:

\(x = 9.36\)