Question
Determine if the given value is a solution of the equation.
15xplus4xplus6equals9; xequalsthree nineteenths
Question content area bottom
Part 1
Is three nineteenths
a solution?
15xplus4xplus6equals9; xequalsthree nineteenths
Question content area bottom
Part 1
Is three nineteenths
a solution?
Answers
GPT-4o mini
To determine if \( x = \frac{3}{19} \) is a solution of the equation \( 15x + 4x + 6 = 9 \), we will substitute \( x \) with \( \frac{3}{19} \) and check if the left side of the equation equals the right side.
1. Combine the terms on the left-hand side:
\[
15x + 4x + 6 = (15 + 4)x + 6 = 19x + 6
\]
2. Substitute \( x \) with \( \frac{3}{19} \):
\[
19 \left(\frac{3}{19}\right) + 6 = 3 + 6 = 9
\]
3. Compare to the right-hand side of the equation:
\[
9 = 9
\]
Since the left side equals the right side when \( x = \frac{3}{19} \), we conclude that \( \frac{3}{19} \) is indeed a solution of the equation.
1. Combine the terms on the left-hand side:
\[
15x + 4x + 6 = (15 + 4)x + 6 = 19x + 6
\]
2. Substitute \( x \) with \( \frac{3}{19} \):
\[
19 \left(\frac{3}{19}\right) + 6 = 3 + 6 = 9
\]
3. Compare to the right-hand side of the equation:
\[
9 = 9
\]
Since the left side equals the right side when \( x = \frac{3}{19} \), we conclude that \( \frac{3}{19} \) is indeed a solution of the equation.