One Step Equations and Inequalities

One Step Equations

One Step equations can be solved in just a single step. Yes, the whole equation can be solved within a single step by either using addition, subtraction, multiplication, or division.

The key to solving these problems is to undo the operation, to isolate the variable. For instance, if the operation is addition, use subtraction (and vice versa) on BOTH sides to undo the operation and isolate the variable. If the operation is division, use multiplication (and vice versa) on BOTH sides to undo the operation and isolate the variable.

Example 1 – Solve for x:

2 * x = 20

Now we have calculated the value of x. To find the value, use the division method to divide by a constant value.

2x / 2 = 20 / 2, so x=10

Example 2 – Solve for n:

n/2 = 8

Here we can use multiplication to use a constant value and multiply in both sides such as:

2 * n/2 = 8 * 2, so n = 16

Example 3 – Solve for x:

x – 10 = 10

To isolate x, we need to undo the operation on the left side. Since it is – 10, we need to add to BOTH sides:

x + 1010 = 10 + 10

x = 20

What is an Inequality?

An inequality is nothing but a mathematical statement where 2 expressions are compared using an inequality sign. In this statement, one expression can be either less or greater than the other expression. In inequality, special symbols are used.

Inequality Signs

Let’s look at some of the inequality signs:

  • a ≠ b means a is not equal to b. Example: 9 ≠ 5
  • a > b a is greater than b. Example: 9 > 6
  • a < b a is lesser than b. Example: 6 < 9
  • a ≥ b a is greater than or equal to b
  • a ≤ b a is lesser than or equal to b

When there is a situation where the solution has more than one acceptable value, then inequalities can be used to represent the situation in hand. Let’s say for example, when you see a sign that says “Speed limit is permitted below 45”, which means the speed limit should be less than 45 or the speed limit is < 45, but the thing is, it doesn’t say whether you should go at the speed limits of 30, 35 or 40. Hence the solution has more than one acceptable value.

Note: If you divide or multiply the inequality expression by a negative number, the direction of the inequality sign changes.

Example 1 – Solve for x:

-2 * x < 20

divide by -2 on both sides. Remember to change the direction of the inequality sign.

2/-2 * x >20/-2

x > -10

“x is greater than -10.”

Example 2 – Solve for x:

n/2 < 8

Multiply by 2 on both sides.

2* n/2 < 8 * 2

n < 16
“n is less than 16.”

Example 3 – Solve for x:

x – 10 > 10

Add `10 on both sides.

x + 1010 > 10 + 10

x > 20

“x is greater than 20.”