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