Download Solving Equations with Variables on Both Sides

Solving Equations with Variables
on Both Sides
Sol A.4
Chapter Lesson 2-4
Step 1 – Use the Distributive Property to
remove any grouping symbols. Use
properties of equality to clear decimals and
fractions.
 Step 2 – Combine like terms on each side of
the equation.
 Step 3 – Use the properties of equality to
get the variable terms on 1 side of the
equation and the constants on the other.
 Step 4 – Use the properties of equality to
solve for the variable.
 Step 5 – Check your solution in the original
equation.

Solving an Equation w/variables on
Both Sides
5x + 2 = 2x + 14
5x – 2x + 2 = 2x - 2x + 14
3x + 2 = 14
3x + 2 – 2 = 14 – 2
3x = 12
(3x)/3 = 12/3
x=4
Your turn
7k + 2 = 4k -10
Solving an Equation with Grouping
Symbols
2(5x – 1) = 3(x + 11)
10x – 2 = 3x + 33
10x - 3x - 2 = 3x - 3x + 33
7x – 2 = 33
7x – 2 + 2 = 33 + 2
7x = 35
(7x)/7 = 35/7
x=5
Your turn
4(2y + 1) = 2(y – 13)
7(4 – a) = 3(a – 4)
An equation that is true for every possible
value of the variable is an identity.
Example x + 1 = x + 1
An equation that has no solution if there is
no value of the variable that makes the
equation true.
Example x + 1 = x + 2 has no solution.
Equations w/Infinitely Many
Solutions (Identity)
10x + 12 = 2(5x + 6)
10x + 12 = 10x + 12
Because 10x + 12 = 10x + 12 is always
true, there are infinitely many solutions of
the equation. The original equation is an
identity.
Equation with No Solution
9m – 4 = -3m + 5 + 12m
9m – 4 = -3m + 12m + 5
9m – 4 = 9m + 5
9m - 9m – 4 = 9m - 9m + 5
-4≠5
Because – 4 ≠ 5, the original
equation has no solution.
Your Turn
3(4b – 2) = - 6 + 12b
2x + 7 = -1(3 – 2x)