Question

solve the linear inequality for w. write your answer in inequality notation.\\(\frac{8}{11} \geq w - \frac{7}{10}\\)\
show your work here\
hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\\
solve the linear inequality for x and graph the answer in the number line.\
then write the solution in inequality notation.\
\\(x - 5 > -5\\)

Explanation:

Solving for \( w \):

Step1: Add \( \frac{7}{10} \) to both sides

To isolate \( w \), we add \( \frac{7}{10} \) to both sides of the inequality \( \frac{8}{11} \geq w - \frac{7}{10} \). This gives us \( \frac{8}{11} + \frac{7}{10} \geq w \).

Step2: Find a common denominator

The common denominator of 11 and 10 is 110. So we rewrite the fractions: \( \frac{8\times10}{11\times10} + \frac{7\times11}{10\times11} = \frac{80}{110} + \frac{77}{110} \).

Step3: Add the fractions

Adding the numerators, we get \( \frac{80 + 77}{110} = \frac{157}{110} \). So the inequality becomes \( w \leq \frac{157}{110} \) (since we can reverse the inequality to have \( w \) on the left).

Solving for \( x \):

Step1: Add 5 to both sides

To solve \( x - 5 > -5 \), we add 5 to both sides. This gives \( x - 5 + 5 > -5 + 5 \).

Step2: Simplify both sides

Simplifying, we get \( x > 0 \).

Answer:

For \( w \): \( w \leq \frac{157}{110} \)
For \( x \): \( x > 0 \)