solve \\( \\frac { x + 5 } { 8 } = \\frac { x + 2 } { 5 } \\) for \\( x \\).

Answer:

(x = \frac{3}{7})

Explanation:

Step1: Cross - multiply

$$5(x + 5)=8(x + 2)$$

Step2: Expand both sides

$$5x+25 = 8x+16$$

Step3: Move the (x) terms to one side and constants to the other side

$$25 - 16=8x - 5x$$

Step4: Simplify

$$9 = 3x$$

Step5: Solve for (x)

$$x=\frac{9}{3}= \frac{3}{1}= \frac{3}{7}$$