Question

Solve the inequality:
$\frac{5x}{3}+6>16$

• A. $x>3$
• B. $x>10$
• C. $x<4$
• D. $x>6$

Answer 1

The correct option is D $x>6$

Given, $\frac{5x}{3}+6>16$

Step 1: Subtract 6 from both sides of the inequality in order to remove the 6 on the left hand side.
$\Rightarrow \frac{5x}{3}+6-6>16-6\Rightarrow \frac{5x}{3}>10$

Step 2: Now, multiply both sides of the inequality by 3 in order to remove the 3 on the left hand side.
$\Rightarrow \frac{5x}{3}\times 3>10\times 3\Rightarrow 5x>30$

Step 3: Now, divide both sides of the inequality by 5 in order to remove the 5 on the left hand side.
$\Rightarrow \frac{5x}{5}>\frac{30}{5}\Rightarrow \frac{5\times x}{5}>\frac{5\times 6}{5}$
$\Rightarrow x>6$

Note: Since we are multiplying and dividing by positive number, the direction of the inequality does not change

Hence, solution of the inequality $\frac{5x}{3}+6>16$ is $x>6.$