1. Solving Linear Equations
By Tristen Billerbeck

2. Warm Up Solve. 1. 2x + 9x – 3x + 8 = 16 2. –4 = 6x + 22 – 4x 3. + = 5
= 5
– = 3
x = 1
x = –13 2 7 x 7 7 1
x = 34 9x 16 2x 4 1 8
x = 50

3. Additional Example 1A: Solving Equations with Variables on Both Sides
Solve.
4x + 6 = x
4x + 6 = x
To collect the variable terms on one side, subtract 4x from both sides.
– 4x – 4x
6 = –3x 6 –3
–3x =
Since x is multiplied by -3, divide both sides by –3.
–2 = x

4. You can always check your solution by substituting the value back into the original equation.
Helpful Hint

5. Check It Out! Example 1A
Solve.
5x + 8 = x
5x + 8 = x
To collect the variable terms on one side, subtract 5x from both sides.
– 5x – 5x
8 = –4x 8 –4
–4x =
Since x is multiplied by –4, divide both sides by –4.
–2 = x

6. Check It Out! Example 1B
Solve.
3b – 2 = 2b + 12
3b – 2 = 2b + 12
To collect the variable terms on one side, subtract 2b from both sides.
– 2b – 2b
b – 2 =
Since 2 is subtracted from b, add 2 to both sides.
b =

7. Check It Out! Example 1C
Solve.
3w + 1 = 3w + 8
3w + 1 = 3w + 8
– 3w – 3w
To collect the variable terms on one side, subtract 3w from both sides.
1 ≠
No solution. There is no number that can be substituted for the variable w to make the equation true.

8. Graphing Calculator Activity p. 17 and 25