Q12. - Algebra 1

Question

Solve each equation. Check your solution.

$9x-4=2x+3$

Step-by-Step Solution

Answer

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

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.