1. 1.4.1 – Solving Linear Equations

2. Unlike expressions, equations have an equal sign, with expressions on both sides Linear = an equation is considered linear if it can be written in the form ax = b – Highest power of x is 1

3. Solving Equations With any equation, we will always try and solve for a specific variable Use inverse operations to complete – What you do to one side, you must do to the other – So, if a number is negative, you would add to both sides

4. Solving Equations Remember, when solving, we will always combine like terms Ultimately, we need to completely isolate (get by itself) the variable of interest – If more than one variable, then the others are treated as constants (IE, real numbers)

5. One-Step Example. Solve the equation x + 6 = -18 for x. Example. Solve 4 – y = 10 for y.

6. One step Example. Solve (x/6) = 4 for x.

7. Multi-Step Example. Solve -5x + 15 = 30 for x. Example. Solve 9 = 4y + 12 for y.

8. Variables on both sides If variables are on both sides, then we must get the variables all to the same side Always look to get variables on the same side, then look to combine any like terms and solve for the variable of interest

9. Example. Solve 2x + 6 = 4x – 10 for x.

10. Example. Solve the equation 4x – 5 = 8x + 7

11. Distributive Property At times, we may have to utilize other properties The distributive property is often need when the variable may be inside a set of paranthesis Still will need to isolate variable to one side; then worry about moving and solving

12. Example. Solve 4(x + 2) = 4(9 – x)

13. Example. Solve 3(w – 6) = -7(w + 4) for w.

14. Assignment 22-32, 37-45 odd, 68, 84