## Answer :

1.

**Combine like terms**to isolate [tex]\(\sin x\)[/tex]:

[tex]\[ 4 + 2 \sin x = 14 - 8 \sin x \][/tex]

Move [tex]\(8 \sin x\)[/tex] to the left side of the equation by adding [tex]\(8 \sin x\)[/tex] to both sides:

[tex]\[ 4 + 2 \sin x + 8 \sin x = 14 \][/tex]

Simplify:

[tex]\[ 4 + 10 \sin x = 14 \][/tex]

2.

**Isolate [tex]\(\sin x\)[/tex]**on one side of the equation:

Subtract 4 from both sides:

[tex]\[ 10 \sin x = 14 - 4 \][/tex]

Simplify:

[tex]\[ 10 \sin x = 10 \][/tex]

Divide both sides by 10:

[tex]\[ \sin x = 1 \][/tex]

3.

**Solve for [tex]\(x\)[/tex]**:

We need to find the value(s) of [tex]\(x\)[/tex] such that [tex]\(\sin x = 1\)[/tex] within the range [tex]\(0^{\circ} \leq x \leq 180^{\circ}\)[/tex].

Recall that [tex]\(\sin x = 1\)[/tex] at [tex]\(x = 90^{\circ}\)[/tex].

Thus,

**the solution**to the equation [tex]\(4 + 2 \sin x = 14 - 8 \sin x\)[/tex] within the specified range is:

[tex]\[ x = 90^{\circ} \][/tex]