An equation is a statement that states that the values of two mathematical expressions are equal. This is represented by an equal sign between the two expressions.
When we have an equation with an unknown variable it is called an Algebraic Equation
To solve an Algebraic equation you must get the variable by itself on one side of the equation in order to solve for the unknown variable. This can be done by doing the following steps depending on the type of equation:
- Adding or subtracting the same value from both sides
- Clear out any fractions by Multiplying every term by the bottom parts
- Divide every term by the same nonzero value
- Combine Like Terms
- Factoring
- Expanding
- Recognizing a pattern
- Apply a function to both sides
Once you solve for the variable make sure you check your solution in the original problem to make sure it equals the same value on both sides of the equation.
Example:
3x - 7 = 11
In this equation you will need to get the X by itself, to do this we would need to do the inverse operation of subtraction by adding seven to both sides of the equation.
3x - 7 + 7 = 11 + 7
This would give us the equation:
3x = 18
This is because when you add 7 to an - 7 they cancel each other out on the left side of the equation. then 11+ 7 = 18
Now to solve 3x = 18, you must divide each side by three because you want to do the inverse operation of the original equation which was multiplying by three.
3x / 3 = 18 / 3
when we divide by three it would leave us with x = 6.
Now that we know x = 6, we must now put it back into the equation in order to check our solution. We would replace the x variable with the number six in the equation.
3(6) - 7 = 11
18 - 7 = 11
11 = 11
This means are solution was correct because both sides equal the same value
Work out this pack of printable translating inequality phrases worksheets and be fluent in translating written descriptions used in real-life scenarios into algebraic inequalities. Here's an instance where it plays out in a sport context — the inequality "p ≥ 5" can be used to denote that the teams with at least 5 points will make it to the next level. Ideal for 6th grade, 7th grade, and 8th grade, our pdf worksheets have sentences that generate one-step and two-step inequalities with integer and rational coefficients and constants. Some of these worksheets are absolutely free!
Writing Algebraic Inequalities From Words | Basic
Let grade 6 kids warm up to the inequality symbols – <, >, ≤, and ≥ – that correspond to these phrases – less than, greater than, less than or equal to, and greater than or equal to – as they do this pdf exercise.
Translating Sentences into Two-Step Inequalities | Easy
The sentences in our printable translating inequality phrases worksheets lead to inequalities of the form px ± q < r or p(x ± q) < r where p, q, and r are integers. Pore over them and construct the apt linear inequalities.