Question

complete the process of solving the equation. fill in all missing terms and select all missing descriptions. simplify any fractions. \\(\frac{x + 19}{5} = 15\\) \\(x + 19 = \square\\) \\(x = \\)

Explanation:

Step1: Multiply both sides by 6

To solve the equation \(\frac{x + 19}{6}=15\), we first multiply both sides of the equation by 6 to eliminate the denominator. Using the multiplication property of equality, if \(\frac{x + 19}{6}=15\), then \(6\times\frac{x + 19}{6}=6\times15\). Simplifying the left - hand side, the 6 in the numerator and denominator cancels out, leaving \(x + 19\) on the left. On the right - hand side, \(6\times15 = 90\). So the equation becomes \(x+19 = 90\).

Step2: Subtract 19 from both sides

To isolate \(x\), we use the subtraction property of equality. Subtract 19 from both sides of the equation \(x + 19=90\). That is, \(x+19 - 19=90 - 19\). Simplifying both sides, the 19 and - 19 on the left - hand side cancel out, and on the right - hand side, \(90-19 = 71\). So \(x = 71\).

Answer:

For the first blank (after \(x + 19=\)): 90 (the description is "Multiply both sides by 6 (Multiplication Property of Equality)")
For the second blank (for \(x=\)): 71 (the description is "Subtract 19 from both sides (Subtraction Property of Equality)")