Q7. - Algebra 1

Question

Solve each equation for the given variable.

$2x-4y=6$ for $x$

Step-by-Step Solution

Answer

The equation for $x$ is $x=2y+3$. 

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 $2x-4y=6$ 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 $4y$ to both sides and then simplify further as shown below,

$$\begin{gathered} 2x-4y=6 \\ 2x-4y+4y=6+4y \end{gathered}$$

Step 3. Simplify further for x .

Simplify the equation and get,

$$\begin{gathered} 2x-4y+4y=6+4y \\ 2x=6+4y\text{ Divide both sides by 2} \\ \frac{2x}{2}=\frac{6+4y}{2}\text{ Simplify} \\ x=2y+3 \end{gathered}$$