Solve 7/11leq7/3(1)+5leq-1

$$\frac{ 7 }{ 11 } \leq \frac{ 7 }{ 3(1)+5 } \leq -1$$

Verify

Solution Steps

Multiply 3 and 1 to get 3.

$$\frac{7}{11}\leq \frac{7}{3+5}\text{ and }\frac{7}{3\times 1+5}\leq -1$$

Add 3 and 5 to get 8.

$$\frac{7}{11}\leq \frac{7}{8}\text{ and }\frac{7}{3\times 1+5}\leq -1$$

Least common multiple of 11 and 8 is 88. Convert \frac{7}{11} and \frac{7}{8} to fractions with denominator 88.

$$\frac{56}{88}\leq \frac{77}{88}\text{ and }\frac{7}{3\times 1+5}\leq -1$$

Compare \frac{56}{88} and \frac{77}{88}.

$$\text{true}\text{ and }\frac{7}{3\times 1+5}\leq -1$$

Multiply 3 and 1 to get 3.

$$\text{true}\text{ and }\frac{7}{3+5}\leq -1$$

Add 3 and 5 to get 8.

$$\text{true}\text{ and }\frac{7}{8}\leq -1$$

Convert -1 to fraction -\frac{8}{8}.

$$\text{true}\text{ and }\frac{7}{8}\leq -\frac{8}{8}$$

Compare \frac{7}{8} and -\frac{8}{8}.

$$\text{true}\text{ and }\text{false}$$

The conjunction of \text{true} and \text{false} is \text{false}.

$$\text{false}$$