3. Example: Solve the equation.
Multiply both sides by 5.
Simplify both sides.
Add –3y to both sides.
Simplify both sides.
Add –30 to both sides.
Simplify both sides.
Divide both sides by 7.

4. Example: Solve the equation.
– 0.01(5a + 4) = 0.04 – 0.01(a + 4)
– 1(5a + 4) = 4 – 1(a + 4)
Multiply both sides by 100.
– 5a – 4 = 4 – a – 4
Apply the distributive property.
– 5a – 4 = – a
Simplify both sides
– 4a – 4 = 0
Add a to both sides and simplify.
– 4a = 4
Add 4 to both sides and simplify.
a = – 1
Divide both sides by -4.

5. Example: Solve the equation.
– 0.01(5a + 4) = 0.04 – 0.01(a + 4)
– 0.05a – 0.04 = 0.04 – 0.01a – 0.04
Apply the distributive property.
– 0.05a – 0.04 = – 0.01a
Simplify both sides.
– 0.04a – 0.04 = 0
Add 0.01a to both sides.
– 0.04a = 0.04
Add 0.04 to both sides and simplify.
a = – 1
Divide both sides by

6. Example: Solve the equation.
5x – 5 = 2(x + 1) + 3x – 7
5x – 5 = 2x x – 7 Use distributive property.
5x – 5 = 5x – Simplify the right side.
– 5 = – Add -5x to both sides.
0 = 0
Add 5 to both sides.
Identity Equation.
Both sides of the equation are identical. This equation will be true for every x that is substituted into the equation, the solution is “all real numbers.”

7. Example: Solve the equation. 3x – 7 = 3(x + 1)
3x – 7 = 3x Use distributive property.
3x + (– 3x) – 7 = 3x + (– 3x) Add –3x to both sides.
– 7 = Simplify both sides.
Contradiction Equation.
Since no value for the variable x can be substituted into this equation that will make this a true statement, there is “no solution.”

8. Solving Linear Equations

9. Examples a) b) c) d)

10. Examples