Question

Solve each equation for the given variable.

$4x-3y=12$for$x$

Short answer

The equation for $x$is $\mathit{x}\mathbf{=}\mathbf{3}\mathbf{+}\frac{\mathbf{3}}{\mathbf{4}}\mathit{y}$.

Step-by-step solution

Step 1. State the concept used.

• To get rid of a number in addition from one side, subtract the same number from both sides of the equal sign.
• To get rid of a number in subtraction from one side, add the same number on both sides of the equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of the equal sign.
• To get rid of a number in the division from one side, multiply the same number on both sides of the equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar signs always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of the larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similarsign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Step 2. Rewrite the equation to solve for x. 

In order to solve the given equation $4x-3y=12$for the variable, isolate the variable term $x$on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate$x$on both sides, first add $3y$to both sides and then simplify furtheras shown below,

$$\begin{gathered} 4x-3y=12 \\ 4x-3y+3y=12+3y \end{gathered}$$

Step 3. Simplify further for x.

Simplify the equation and get,

$$\begin{gathered} 4x-3y+3y=12+3y \\ 4x=12+3y\text{Dividebothsidesby4} \\ \frac{4x}{4}=\frac{12+3y}{4}\text{Simplify} \\ x=3+\frac{3}{4}y \end{gathered}$$