Solve for \(x\) in \(14+1\times x-5=3x+27-10\).
Solve for \(x\).
\[14+1\times x-5=3x+27-10\]
Simplify \(1\times x\) to \(x\).
\[14+x-5=3x+27-10\]
Simplify \(14+x-5\) to \(x+9\).
\[x+9=3x+27-10\]
Simplify \(3x+27-10\) to \(3x+17\).
\[x+9=3x+17\]
Subtract \(x\) from both sides.
\[9=3x+17-x\]
Simplify \(3x+17-x\) to \(2x+17\).
\[9=2x+17\]
Subtract \(17\) from both sides.
\[9-17=2x\]
Simplify \(9-17\) to \(-8\).
\[-8=2x\]
Divide both sides by \(2\).
\[-\frac{8}{2}=x\]
Simplify \(\frac{8}{2}\) to \(4\).
\[-4=x\]
Switch sides.
\[x=-4\]
\[x=-4\]
Substitute \(x=-4\) into \(10r\times 14-(x+5)=3(x+9)-10\).
Start with the original equation.
\[10r\times 14-(x+5)=3(x+9)-10\]
Let \(x=-4\).
\[10r\times 14+4-5=3(-4+9)-10\]
Simplify.
\[140r-1=5\]
\[140r-1=5\]
Solve for \(r\) in \(140r-1=5\).
Solve for \(r\).
\[140r-1=5\]
Add \(1\) to both sides.
\[140r=5+1\]
Simplify \(5+1\) to \(6\).
\[140r=6\]
Divide both sides by \(140\).
\[r=\frac{6}{140}\]
Simplify \(\frac{6}{140}\) to \(\frac{3}{70}\).
\[r=\frac{3}{70}\]
\[r=\frac{3}{70}\]
Therefore,
\[\begin{aligned}&r=\frac{3}{70}\\&x=-4\end{aligned}\]
r=3/70;x=-4
