for what values of x is the inequality below true? 8x - \\frac{43}{8} < - 3(x + \\frac{4}{3}) a. x >…

for what values of x is the inequality below true? 8x - \\frac{43}{8} < - 3(x + \\frac{4}{3}) a. x > \\frac{1}{8} b. x < \\frac{1}{8} c. x > \\frac{15}{8} d. x < \\frac{15}{8}

for what values of x is the inequality below true? 8x - \\frac{43}{8} < - 3(x + \\frac{4}{3}) a. x > \\frac{1}{8} b. x < \\frac{1}{8} c. x > \\frac{15}{8} d. x < \\frac{15}{8}

Answer

Explanation:

Step1: Expand the right - hand side

Expand $-3(x+\frac{4}{3})$ to get $-3x - 4$. So the inequality becomes $8x-\frac{43}{8}<-3x - 4$.

Step2: Move the $x$ terms to one side

Add $3x$ to both sides: $8x + 3x-\frac{43}{8}<-4$, which simplifies to $11x-\frac{43}{8}<-4$.

Step3: Move the constant terms to one side

Add $\frac{43}{8}$ to both sides: $11x<-4+\frac{43}{8}$. Calculate $-4+\frac{43}{8}=\frac{-32 + 43}{8}=\frac{11}{8}$. So $11x<\frac{11}{8}$.

Step4: Solve for $x$

Divide both sides by 11: $x<\frac{11}{8}\div11=\frac{11}{8}\times\frac{1}{11}=\frac{1}{8}$.

Answer:

B. $x<\frac{1}{8}$