This unit covers solving multi-step equations that are not of the standard multi-step equations' form. Inverse operations will be used to solve each equation, while PEMDAS will be used to check the answer. Solving equations can be simple if you stick to the tried and true techniques to solve an equation.
Example 1:
Solve: 2(3x + 5) = 34
6x + 10 = 34 Distributive Property with the 2
6x = 34 - 10 Subtract 10 from both sides
6x = 24 Simplify. Divide both sides by 6
x = 4 Answer
Example 2:
Solve: 3(x + 3) - 4(x + 5) = -14
3x + 9 - 4x - 20 = -14 Distributive property two times
3x - 4x + 9 - 20 = -14 Re-arrange like terms
-1x - 11 = -14 Combine like terms
-1x = -14 + 11 Add 11 to both sides
-1x = -3 Divide both sides by -1
x = 3 Answer
Check the solution. It is very important to remember to use PEMDAS for this part:
3(x + 3) - 4(x + 5) = -14
3(3 + 3) - 4(3 + 5) = -14
3(6) - 4(8) = -14
18 - 32 = -14
-14 = -14 ★
Example 3:
Solve: 1/2 (x + 4) + 2(x - 9) = -1
1/2x + 2 + 2x - 18 = -1 Distributive property two times
1/2x + 2x + 2 - 18 = -1 Re-arrange like terms
2.5x - 16 = -1 Combine like terms
2.5 x = -1 + 16 Add -16 to both sides
2.5x = 15 Simplify
x = 15 ÷ 2.5 Divide both sides by 2.5
x = 6 Answer
Check the solution:
1/2 (x + 4) + 2(x - 9) = -1
1/2(6 + 4) + 2(6 - 9) = -1 Substitution x = 6
1/2(10) + 2(-3) = -1 PEMDAS
5 + -6 = -1
-1 = -1 ★
Example 4:
Solve: 5x + 2(x - 4) + 6 = 12
5x + 2x - 8 + 6 = 12
7x -2 = 12
7x = 14
x = 14 ÷ 7
x = 2 Answer
Check the solution:
5x + 2(x - 4) + 6 = 12
5(2) + 2(2 - 4) + 6 = 12
10 + 2(-2) + 6 = 12
10 - 4 + 6 = 12
6 + 6 = 12
12 = 12 ★
Now you do the next problem on your own. Check your answer to make sure it's correct.
Solve: 5(x + 2) + 4(x - 3) + 2(x - 5) = 98