What is the largest integer $x$ such that $\frac{x}{3}+\frac{4}{5} < \frac{5}{3}$?
+9466 \(\frac{x}{3}+\frac{4}{5} < \frac{5}{3}\)
Subtract \(\frac45\) from both sides of the inequality.
\(\frac{x}{3}+\frac{4}{5}{\color{blue}-\frac45} < \frac{5}{3}{\color{blue}-\frac45}\)
\(\frac{x}{3} < \frac{5}{3}-\frac45\)
Get a common denominator on the right side.
\(\frac{x}{3} < \frac{5}{3}\cdot\frac55-\frac45\cdot\frac33\)
\(\frac{x}{3} < \frac{25}{15}-\frac{12}{15}\)
Combine the fractions on the right side.
\(\frac{x}{3} < \frac{13}{15}\)
Multiply both sides by 3 , a positive number.
\(\frac{x}{3}{\color{blue}\cdot3} < \frac{13}{15}{\color{blue}\cdot3}\)
\(x < \frac{39}{15}\)
And \(\frac{39}{15}\) = 2.6
\(x <2.6\)
What is the largest integer x such that x < 2.6 ?
What is the largest integer less than 2.6 ?
The largest integer less than 2.6 is 2 , so
x = 2
