Question

solve the inequality. graph the solution set and write it in interval - notation.
\\(\frac{1}{5}(x + 5)<\frac{1}{7}(3x + 4)\\)
choose the correct graph below.
write the answer in interval notation.
(type your answer in interval notation. use integers or fractions for)

Explanation:

Step1: Eliminate fractions

Multiply both sides by 35 (LCM of 5 and 7) to get $7(x + 5)<5(3x + 4)$.

Step2: Expand expressions

Expand both sides: $7x+35 < 15x + 20$.

Step3: Isolate x - terms

Subtract 7x from both sides: $35<15x - 7x+20$, which simplifies to $35 < 8x+20$.

Step4: Further isolate x

Subtract 20 from both sides: $35 - 20<8x$, so $15 < 8x$.

Step5: Solve for x

Divide both sides by 8: $x>\frac{15}{8}$.

Answer:

The correct graph is the one with an open - circle at $\frac{15}{8}$ and the line extending to the right. In interval notation, the solution is $(\frac{15}{8},\infty)$.