Determine whether $$ \frac{3 x-17}{8 x-17}=\frac{3}{8} $$ is true. True False

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UpStudy AI · Accepted Answer

Solve the equation $$ \frac{3x-17}{8x-17}=\frac{3}{8} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{3x-17}{8x-17}=\frac{3}{8}$$
- step1: Find the domain:
  $$\frac{3x-17}{8x-17}=\frac{3}{8},x
eq \frac{17}{8}$$
- step2: Cross multiply:
  $$\left(3x-17ight)	imes 8=\left(8x-17ight)	imes 3$$
- step3: Simplify the equation:
  $$8\left(3x-17ight)=3\left(8x-17ight)$$
- step4: Calculate:
  $$24x-136=3\left(8x-17ight)$$
- step5: Calculate:
  $$24x-136=24x-51$$
- step6: Move the expression to the left side:
  $$24x-136-\left(24x-51ight)=0$$
- step7: Calculate:
  $$-85=0$$
- step8: The statement is false:
  $$x \in \varnothing $$
- step9: Check if the solution is in the defined range:
  $$x \in \varnothing ,x
eq \frac{17}{8}$$
- step10: Find the intersection:
  $$x \in \varnothing $$
The equation $$ \frac{3x-17}{8x-17}=\frac{3}{8} $$ has no solution, which means it is not true. Therefore, the statement is false.
The statement is false.

Determine whether is true.
True
False

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