An equation is a balance
Use inverse operations to isolate the variable. Whatever you add, subtract, multiply, or divide on one side must also happen on the other.
Example becomes after subtracting from both sides.
Chapter 07 of 10
Equations & Inequalities
How can an unknown value be found while keeping a statement balanced?
An equation states that two expressions are equal. An inequality compares values and usually has many solutions. Both are solved by undoing operations while applying the same change to each side.
The big ideas
Understand these before you worry about speed.
Multiplication and division undo each other
A coefficient means multiplication. Divide both sides by the coefficient; for a divided variable, multiply both sides by the divisor.
Example gives , while gives .
Inequalities describe sets of values
An open circle excludes the endpoint for < or >. A closed circle includes it for ≤ or ≥. Shade in the direction of the solutions.
Example includes and every number to its left.
Check a solution in the original statement
Substitute the value for the variable and confirm that the result is true. For an inequality, test a value from the shaded region.
ExampleFor , checks because .
Worked example
Follow the reason for each step—not just the symbols.
Problem
A number divided by , then increased by , equals . Find the number.
- Write the equation .
- Subtract from both sides: .
- Multiply both sides by : .
- Check: .
Answer
Try it yourself
Work on paper first. Open each answer only when you are ready to check.
1
Solve .
Check answer
2
Solve .
Check answer
3
Solve .
Check answer
4
Graph on a number line.
Check answer
Open circle at ; shade right.Practice and tools
Use the resource that matches what you need next.