Question

Solve each equation. Check your solution.

$9x-4=2x+3$

Short answer

The solution of the given equation is $x=1$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$9x-4=2x+3$”.

Step 2. Solve the given equation.

Solving,

$9x-4=2x+3$ (Given equation)

$9x-4-2x=2x+3-2x$ (Subtract $2x$from both sides)

$7x-4=3$ (Simplify)

$7x-4+4=3+4$ (Add 4 to both sides)

$7x=7$ (Simplify)

$\frac{7x}{7}=\frac{7}{7}$ (Divide both sides by 7)

$x=1$ (Simplify)

So, $x=1$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $x=1$in the given equation $9x-4=2x+3$to get,

$\begin{array}{l}9\left(1\right)-4=2\left(1\right)+3\\ 9-4=2+3\\ 5=5\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.