Write down the original equation first.
Solve the part of the equation inside parenthesis and brackets first. For example if you have [5(4x-2x)]-10=20, first perform the part of the equation inside the parenthesis, then the part of the equation inside the brackets, then the rest. So for example 4x-2x=2x and then 5(2x)=10x, you end up with 10x-10=20.
Simplify one or both sides of the equation when possible. So with our prior example of 10x-10=20, we must add 10 to both sides to simplify. 10x-10+10=20+10 or 10x=30.
Always perform a simplifying action to both sides. A simplifying action must always be the opposite action. If the original equation adds five, to simplify you will subtract five from both sides. In our example we have 10x=30, and so must divide both sides by 10 to isolate our variable and solve for x=3. If we had an example with a fraction or division such as 1/10x=3 we would have to multiple by 10 to solve for x.
Check your solution with a calculator, just in case, by plugging the variable you isolated into the equation. In our case, we would plug in the value of 3 for x in the original equation [5(4x-2x)]-10=20, which would become [5(4X3-2X3)]-10=20 or [5(12-6)]-10=20, which works out perfectly 5X6=30,30-10=20.
If you have a real-life situation and you want to solve for an unknown, make the unknown a letter variable, like x, and plug in the numbers available to you. For example, you have a job delivering papers for the local newspaper. You earn $10 per day, plus $2 for each delivery. You want to earn a minimum of $50 per day.
Add $10 per day, to $2 times the number of papers you deliver or x, equal to 50. 10+1x=50. Subtract 10 from both sides and you have 2x=40.
Solve for how many papers you need to deliver, by dividing by 2. 2x/2=40/2 or x=20. To make $50, you must deliver a minimum of 20 papers.
Write another multi-step equation with ages. Tim is 8 years older than David. David is 14 years older than Carmen. If the sum of all three ages is 90, how old are is Carmen.
Define x as Carmen, the minimum age. David is x+14, and Tim is x+14+8. Combine the three into your initial equation equaling 90: x+x+14+x+14+8=90.
Combine like values. x+x+x and real numbers 14+14+8 into a simplified equation 3x + 36=90.
Subtract 36 from both sides. 3x+36-36=90-36 and you get 3x=54.
Divide both sides of the equation by 3 to solve for x. X=18. So Carmen=18, David=18+14=32, and Tim=18+14+8=40.
Check your answer by adding the three together, 18+32+40=90.