Question

1. if tv = 14x - 8, find tu.

Explanation:

Step1: Set up equation

Since $TV=TU + UV$, we have $14x - 8=(9x + 2)+5$.

Step2: Simplify right - hand side

$(9x + 2)+5=9x+7$, so the equation becomes $14x - 8=9x + 7$.

Step3: Isolate x terms

Subtract $9x$ from both sides: $14x-9x - 8=9x-9x + 7$, which simplifies to $5x-8 = 7$.

Step4: Solve for x

Add 8 to both sides: $5x-8 + 8=7 + 8$, getting $5x=15$. Then divide both sides by 5: $x=\frac{15}{5}=3$.

Step5: Find TU

Substitute $x = 3$ into the expression for $TU$ which is $9x + 2$. So $TU=9\times3+2=27 + 2=29$.

Answer:

29