Question

Solve each equation for the given variable.

$y-2=x+3$for$y$

Short answer

The equation for $y$is $\mathit{y}\mathbf{=}\mathit{x}\mathbf{+}\mathbf{5}$.

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 y. 

In order to solve the given equation $y-2=x+3$for the variable, isolate the variable term $y$on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate$y$on both sides, first, add 2 to both sides and then simplify furtheras shown below,

role="math" localid="1647497993228" $$\begin{gathered} y-2=x+3 \\ y-2+2=x+3+2 \end{gathered}$$

Step 3. Simplify further for y.

Simplify the equation and get,

$$\begin{gathered} y-2=x+3 \\ y-2+2=x+3+2 \\ y=x+5 \end{gathered}$$