Question

For which of the following linear equation(s) is $x=6$ a solution?

• A. $3x+5=4x-1$
• B. $x-5x=6$
• C. $\frac{x-3}{x+3}=\frac{2}{6}$
• D. $5x=6x+6$

Answer 1

Answer: (A), (C)

The correct options are
A $3x+5=4x-1$
C $\frac{x-3}{x+3}=\frac{2}{6}$

Solving the equation, $3x+5=4x-1$, we get
$3x+5=4x-1\Rightarrow -x=-6\Rightarrow x=6$

Solving the equation, $x-5x=6$, we get
$x-5x=6\Rightarrow -4x=6\Rightarrow x=-\frac{6}{4}$

Solving the equation, $\frac{x-3}{x+3}=\frac{2}{6}$, we get
$\frac{x-3}{x+3}=\frac{2}{6}\Rightarrow 6(x-3)=2(x+3)\Rightarrow 6x-18=2x+6\Rightarrow 4x=24\Rightarrow x=\frac{24}{4}\Rightarrow x=6$

Solving the equation, $5x=6x+6$, we have
$5x=6x+6\Rightarrow 5x-6x=6\Rightarrow -x=6\Rightarrow x=-6$

$\therefore$ The linear equations with solution $x=6$ are $3x+5=4x-1$ and $\frac{x-3}{x+3}=\frac{2}{6}$.

Alternate solution:
We can simply substitute $x=6$ in the given equations and check whether it satisfies the equation or not.

For $3x+5=4x-1$, substituting $x=6$, we get
$3\left(6\right)+5=4\left(6\right)-1$
$\Rightarrow$ 23 = 23
LHS = RHS
Hence $x=6$ is a solution for this equation.

For $\frac{x-3}{x+3}=\frac{2}{6}$ , substituting $x=6$, we get
$\frac{6-3}{6+3}=\frac{2}{6}$

$\Rightarrow$ $\frac{3}{9}=\frac{2}{6}$

$\Rightarrow$ $\frac{1}{3}=\frac{1}{3}$

LHS = RHS
Hence $x=6$ is a solution for this equation.
For all the other options, it can be seen that $x=6$ is not a solution.