Learn to solve for an unknown value by keeping an equation balanced, and apply this to real word problems.
An equation stays balanced as long as you do the same operation to both sides. To solve for x, isolate it by undoing whatever operations are being applied to it, working in reverse order.
Solve: x + 7 = 15
Subtract 7 from both sides: x = 8
Solve: 3x − 4 = 11
Add 4 to both sides: 3x = 15, then divide by 3: x = 5
Many word problems can be solved by translating the situation into an equation — assigning a letter to the unknown, writing an equation based on the given information, then solving it.
A number increased by 9 gives 24. Find the number.
Let the number be x. x + 9 = 24, so x = 15
Three times a number, decreased by 5, is 16. Find the number.
Let the number be x. 3x − 5 = 16, so 3x = 21, x = 7
1. Solve: x − 6 = 12
2. Solve: 2x + 5 = 17
3. Solve: 4x − 3 = 21
4. A number decreased by 8 gives 15. Find the number.
5. Twice a number, increased by 7, is 25. Find the number.