Q9. - Algebra 1

Question

Solve each equation for the given variable.

$4x-3y=12$ for $x$

Step-by-Step Solution

Answer

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

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 similar sign 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 further as 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,

$$\begin{gathered} 4x-3y+3y=12+3y \\ 4x=12+3y\text{ Divide both sides by 4} \\ \frac{4x}{4}=\frac{12+3y}{4}\text{ Simplify} \\ x=3+\frac{3}{4}y \end{gathered}$$