SOLVING SIMPLE EQUATIONS WITH LIKE TERMS
In previous tutorials, You have solved equations using the 4 methods, addition, subtraction, divide, multiply:Now, you will solve equations that have more than 1 like term; we solve this type of equation by First combining the like terms in the equation, and then using the opposite method to solve.
HOW TO SOLVE SIMPLE EQUATIONS THAT HAVE LIKE TERMS
When one side of the equation has like terms, we first combine them, then we solve by using the
opposite method: If your equation is addition we use the subtraction method to begin solving
If your equation is subtraction, we use the addition method to begin solving
Then use the divide method to complete and solve.
EXAMPLE When Solving Equation with Like Terms
1x + 10 + 3x = 30 The left side of this equation has 1x and 3x as like terms, so we first combine them.4x + 10 = 30 Now we can use the opposite of what`s in the equation to solve it, as addition is being used in the equation, we use subtraction method to solve
4x + 10 -10 = 30 - 10 We subtract 10 from each side of the equation
4x = 20 Now we must solve this equation, as it is multiply we use opposite, divide to solve
4x /4 = 20 / 4 Place the 4 as a fraction on each side of the equation
x = 5 Now verify your answer by replacing 5 with x in the equation
1 (5) + 10 + 3 (5) = 30
5 + 10 + 15 = 30
30 = 30 Each side is the same result so your answer is correct
PRACTICE EQUATIONS
Solve Each Equation By First Combining the Like Terms
4x + 6 + 1x = 364 - 3x - 6x = 41
1x + 3x+ 3 = 21
ANSWERS With Explanations
4x + 6 + 1x = 36 First, combine the like terms
5x + 6 = 36 Now subtract 6 from each side of the equation
5x + 6 - 6 = 36 - 6
5x = 30 Now we divide each side of the equation by 5
5x / 5 = 30 /5
x =6 To verify your answer replace x with 6 in the equation
4 (6) + 6 + 1 (6) = 36
24 + 6 + 6 = 36
36 = 36 Each side of the equation has same result, your answer is correct
4 - 3x - 6x = 41 First combine the like terms
4 - 9x = 41 Now we use the opposite of what`s in the equation to solve it, as subtraction is being used in the equation, we use addition method to solve
9x - 4 + 4 = 41 + 4 Add 4 to each side of the equation
9x = 45
Now divide each side of the equation by 9
9x / 9 = 45 / 9
x = 5 To verify your answer, replace x in the equation with 5
4 - 3(5) - 6(5) = 41
4 - 15 - 30 = 41 In algebra, when subtracting we add, -11 - 30,
11 + 30 = 41
41 = 41 Each side of the equation has same result, your answer is correct
1x + 3x+ 3 = 21 1x + 3x + 3 = 19
First combine the like terms
4x + 3 = 19
Now we use subtraction method as the equation has addition; subtract 3 from each side
4 x + 3 - 3 = 19 - 3
4x = 16 Now we divide each side of the equation by 4
4x / 4 = 16 / 4
x = 4 To verify replace x in the equation with 4
1(4) + 3(4) + 3 = 19
4 + 12 + 3 = 19
19 = 19 Each side of equation has same result, answer is correct
Solve Equations
By Using Distributive Property to Remove Brackets and Then Combine Like Terms
EXAMPLE:If your equation has brackets, 1(5x + 2x + 4) = 25; you must remove them first
Use the distributive property;5x + 2x + 4 = 25 to remove the brackets
Then, Combine the like terms; 7x + 4 = 25
Then solve the equation by using your opposite method; We use subtraction method, as the equation is addition Subtract from each side of the equation
7x + 4 - 4 = 25 - 4
7x = 21
7x/7 = 21 / 7 Now use the divide method to complete the equation solving:
x = 3
And to verify you have the correct answer, replace x in the equation with 3
5(3) + 2(3) + 4 = 25
15 + 6 + 4 = 25
25 = 25 Each side has same result, so your answer is correct
Solve Equations With 2 Methods
You now know how to solve equations when brackets have to be removed first. You have to use the distributive property to
first remove the brackets (), then solve the equation using
2 methods, subtract or addition method first; then the divide method. This same rule applies when solving equations with more than one term in them.
EXAMPLE; To solve x + 7 = 14, you need only use 1 method to solve this equation- the subtraction method.
EXAMPLE; To solve 4x + 18 = 66, you need to use 2 methods to solve the equation. First the subtraction method is used, then the divide method.
WHY Because we have to get the variable x by itself on one side of the equation; and to do so, we need to use the 2nd divide method.
Let`s solve each equation:
x + 7 = 14,
x + 7 - 7 = 14 - 7 First we use the opposite method to solve, as the equation has addition, we use subtraction to solve; Subtract 7 from each side of the equation
x = 7 To verify you have the correct answer, replace x in the equation with the 7
7 + 7 = 14
14 = 14 Each side of the equation equals the other, so the answer is correct.
We were able to solve this equation with one method (subtraction) because the equation had only 1 term on the left side.
To solve
4x + 18 = 66, this equation, we will need to use 2 methods, as the left side of equation has 2 terms.(the variable x has a number 4x) First, we use the opposite method to begin solving: the equation has addition, so we use subtraction, subtract 18 from each side
4x + 18 - 18 = 66 - 18
4x = 48
Now we have completed 1 method, but we still have a term on the left side of the equation, we have to get the x by itself; in order to so that we must use another method,this time the divide method
We place the 4x as a fraction with 4 and add that 4 to each side of the equation
4x / 4 = 48 / 4
x = 12 Now the equation is solved, x is by itself. Now you can verify your answer; replace 12 where x is in the equation.
4(12) + 18 = 66
48 + 18 = 66
66 = 66 Each side equals the other, the answer is correct.
FYI WHEN SOLVING EQUATIONS
Remove any brackets from the equation (), use the distributive property
Combine like terms on each side of the equation
Use opposite method to get the constants on one side of equation, and variables on the other side of equation
Use 2nd solving method - divide - if necessary (when equation has more than 1 term)
Solve for x,
Verify your equation, replace x with the answer