Solving complex equations (positive numbers only)

By complex (composite) equations, we mean equations that contain two or more arithmetic operations.

The solution of such equations is performed according to the same rules that we considered on the page “Solving simple equations of grade 5” in the same topic. But the solution of compound equations is made in a certain sequence.

Consider the equation:

1. Set the order of actions in the equation.
2. We determine the unknown by the last action. The last action in this equation is subtraction. We draw your attention to the fact that at this stage our unknown is “5y”, and that is what we regard as decreasing.
3. We solve as a simple equation and find “5y”. Recall the rule for finding the unknown diminishing.
   
   

   To find the unknown deductible, add the deductible to the difference.

   
4. Now we have a simple equation. Need to find an unknown multiplier. We solve the equation according to the following rule.
   
   

   To find an unknown factor, it is necessary to divide the product into a known factor.

   
5. Do not forget to check.

That's right. So the equation is solved correctly.

Another way to solve complex equations

Some complex (composite equations) can be solved in another way. Knowing and being able to apply the properties of addition and subtraction, as well as the properties of multiplication and division, the equations are solved as follows.

Consider the equation.

(x + 54) - 28 = 38

1. We simplify the expression on the left side of the equation, using one of the properties of subtraction.
   
   

   To subtract a number from the sum, you need to subtract this number from one term and add the result of the subtraction to the other term.

   
2. Next, we solve a simple equation using the rule for finding the unknown term.
   
   x = 38 - 26
   
   x = 12
3. Perform a check.
   
   (12 + 54) - 28 = 38
   
   66 - 28 = 38
   
   38 = 38

Simplification of expressions in equations

Solve the equation.

5x + 2x = 49

The left side of the equation can be simplified. Let's do it.

7x = 49

Now we solve a simple equation according to the rule of finding an unknown factor.

x = 49: 7

x = 7

After completing the example, run the check.