Question

solve and check the equation. 3(3 - 5x)=2(5x + 4) select the correct choice below and, if necessary, fill in any answer box to complete your answer. a. the solution set is b. the solution set is {x|x is a real number} c. the solution set is ∅

Explanation:

Step1: Expand both sides

Expand $3(3 - 5x)$ to get $9-15x$, and expand $2(5x + 4)$ to get $10x+8$. So the equation becomes $9-15x=10x + 8$.

Step2: Move terms with x to one - side

Add $15x$ to both sides: $9=10x + 8+15x$, which simplifies to $9 = 25x+8$.

Step3: Isolate the term with x

Subtract 8 from both sides: $9 - 8=25x$, so $1 = 25x$.

Step4: Solve for x

Divide both sides by 25: $x=\frac{1}{25}$.

Step5: Check the solution

Substitute $x = \frac{1}{25}$ into the original equation.
Left - hand side: $3(3-5\times\frac{1}{25})=3(3-\frac{1}{5})=3\times\frac{14}{5}=\frac{42}{5}$.
Right - hand side: $2(5\times\frac{1}{25}+4)=2(\frac{1}{5}+4)=2\times\frac{21}{5}=\frac{42}{5}$.
Since the left - hand side equals the right - hand side when $x=\frac{1}{25}$, the solution set is $\{x|x=\frac{1}{25}\}$.

Answer:

B. The solution set is $\{x|x=\frac{1}{25}\}$