Question

solve the equation.
$\displaystyle -\frac{3}{5}x + 37 = -17$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\\(\bigcirc\\) a. the solution is \\(x = \square\\) (type an integer or a decimal.)
\\(\bigcirc\\) b. the solution is all real numbers.
\\(\bigcirc\\) c. there is no solution.

Explanation:

Step1: Subtract 37 from both sides

To isolate the term with \( x \), we subtract 37 from both sides of the equation \( -\frac{3}{5}x + 37 = -17 \). This gives us \( -\frac{3}{5}x + 37 - 37 = -17 - 37 \), which simplifies to \( -\frac{3}{5}x = -54 \).

Step2: Solve for \( x \)

To solve for \( x \), we multiply both sides of the equation \( -\frac{3}{5}x = -54 \) by the reciprocal of \( -\frac{3}{5} \), which is \( -\frac{5}{3} \). So, \( x = -54 \times (-\frac{5}{3}) \). Calculating this, we have \( x = \frac{270}{3} = 90 \).

Answer:

A. The solution is \( x = 90 \)