One-Step Equations

One-step equations are used to solve for the unknown variable. 

Example:

x + 2 = 10

x = 8, where x is the unknown variable.

To solve these equations, we need to isolate the variable to one side and the constants to the other side of the equal sign. In the above equation, when 2 was moved to the other side, its sign changed from positive to negative. So, 10 - 2 = 8.

A one-step equation is all about applying the inverse of the operation given in the equation. For example, if the given operation is addition, then we should change the operation to subtraction while solving a one-step equation. Here are some common operations and their inverse function: 

To solve a one-step equation that has either addition or subtraction as its operation, we need to follow a basic rule. The rule is that whenever a constant or variable is shifted from either the RHS to the LHS or vice versa, its operation changes to its inverse.

For example, in the equation x - 2 = 8, when -2 is shifted from LHS to RHS, the equation becomes x = 8 + 2. Now, we have isolated x and can proceed to find its value, which is 10.  

Similarly, if the equation is x + 2 = 8, then we can rewrite the equation as x = 8 - 2. Here, we have isolated x, and while shifting + 2 from the LHS of the equation to the RHS, its operation changes from +2 to -2. So the value of x is: x = 8 - 2 = 6. 

To solve a one-step equation involving multiplication or division, just change the operation to its inverse while isolating the variable.

• If the variable is multiplied, we will divide it.

• If the variable is divided, we will multiply it.

Example:

1. Solve: 5x = 25

Here, 5 is multiplied, so we divide both sides by 5.

5x ÷ 5 = 25 ÷ 5

x = 5

2. Solve: x ÷ 7 = 2

Since x is divided by 7, multiply both sides by 7.

x ÷ 7 × 7 = 2 × 7

x = 14

One-step equations are not only used in solving math problems; they are also useful in everyday life. These equations help us find the unknown values quickly by performing the basic mathematical operations. Here are some of the real-life examples where one-step equations are used.

Shopping and Budgeting: While shopping and budgeting, if we know how much we spent and how much money we had at first, we can find out how much money is left. For example, if we had Rs. 500 before purchasing a bag for Rs. 120, we would have Rs. 380 remaining. How did we land at 380? Let’s look at the equation below. 

Equation: x = 500 - 120
x = Rs. 380

Cooking and Recipes: We can use equations to adjust the amount of ingredients while cooking. If you need 3 cups of flour for 1 cake, then how much flour do you need for 4 cakes?

Equation: x = 3 × 4
x = 12 cups

Distance or Speed: One-step equations can help us find speed when distance and time are known. For example, if you travel 60 km in 3 hours, what is your speed per hour? To solve this problem, we use the formula: Speed = Distance/Time
So the equation is x = 60 ÷ 3
x = 20 km/h.