1.4.1 – solving linear equations. unlike expressions, equations have an equal sign, with...

1.4.1 – Solving Linear Equations

• 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

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

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)

One-Step

• Example. Solve the equation x + 6 = -18 for x.

• Example. Solve 4 – y = 10 for y.

One step

• Example. Solve (x/6) = 4 for x.

Multi-Step

• Example. Solve -5x + 15 = 30 for x.

• Example. Solve 9 = 4y + 12 for y.

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

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

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

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

• Example. Solve 4(x + 2) = 4(9 – x)

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

• Assignment• 22-32, 37-45 odd, 68, 84