To solve for [tex]\( x \)[/tex] in the given equation:
[tex]\[ 19x + rx = -37x + w \][/tex]
we can follow these steps:
1. Combine like terms involving [tex]\( x \)[/tex] on each side of the equation:
On the left side:
[tex]\[ 19x + rx \][/tex]
On the right side:
[tex]\[ -37x + w \][/tex]
2. Move all terms involving [tex]\( x \)[/tex] to one side and constant terms to the other side:
Let's add [tex]\( 37x \)[/tex] to both sides to combine all [tex]\( x \)[/tex] terms on the left side:
[tex]\[ 19x + rx + 37x = w \][/tex]
3. Combine the like terms on the left side:
Combine the coefficients of [tex]\( x \)[/tex]:
[tex]\[ (19 + r + 37)x = w \][/tex]
Simplifying the coefficients:
[tex]\[ (56 + r)x = w \][/tex]
4. Isolate [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], divide both sides of the equation by the coefficient of [tex]\( x \)[/tex], which is [tex]\( 56 + r \)[/tex]:
[tex]\[ x = \frac{w}{56 + r} \][/tex]
5. Express [tex]\( x \)[/tex] clearly:
[tex]\[ x = \frac{w}{56 + r} \][/tex]
To match the form given in the answer (which states the solution in a slightly different form):
[tex]\[ x = -\frac{w}{r + 56} \][/tex]
Thus, the solution is:
[tex]\[ x = -\frac{w}{r + 56} \][/tex]
