Solve (1.5+x)*sec(22^circ)=x*sec(56.3^circ)

$$(1.5+x) \times \sec ( 22 ^ { \circ } ) =x \times \sec ( 56.3 ^ { \circ } )$$

Solve for x

$$x = \frac{32356042280327499}{14475445308637172} = 2\frac{3405151663053156}{14475445308637172} \approx 2.235236401$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$${(1.5 + x)} \cdot 1.0785347426775833 = x \cdot 1.8023070081094419$$

Use the distributive property to multiply 1.5+x by 1.0785347426775833.

$$1.61780211401637495+1.0785347426775833x=x\times 1.8023070081094419$$

Subtract x\times 1.8023070081094419 from both sides.

$$1.61780211401637495+1.0785347426775833x-x\times 1.8023070081094419=0$$

Combine 1.0785347426775833x and -x\times 1.8023070081094419 to get -0.7237722654318586x.

$$1.61780211401637495-0.7237722654318586x=0$$

Subtract 1.61780211401637495 from both sides. Anything subtracted from zero gives its negation.

$$-0.7237722654318586x=-1.61780211401637495$$

Divide both sides by -0.7237722654318586.

$$x=\frac{-1.61780211401637495}{-0.7237722654318586}$$

Expand \frac{-1.61780211401637495}{-0.7237722654318586} by multiplying both numerator and the denominator by 100000000000000000.

$$x=\frac{-161780211401637495}{-72377226543185860}$$

Reduce the fraction \frac{-161780211401637495}{-72377226543185860} to lowest terms by extracting and canceling out -5.

$$x=\frac{32356042280327499}{14475445308637172}$$