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Solving Linear Equations

Solving Linear Equations. One-step equations Multi-step equations Variable on both sides. To solve an equation. Means to isolate the variable having a coefficient of 1 on one side of the equation Remember, x means 1 times X So then the coefficient of x is 1.

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Solving Linear Equations

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  1. Solving Linear Equations One-step equations Multi-step equations Variable on both sides

  2. To solve an equation • Means to isolate the variable having a coefficient of 1 on one side of the equation • Remember, x means 1 times X So then the coefficient of x is 1

  3. I. Equations with one operation Y + 7 = 4 To solve this equation for y, you must subtract 7 on both sides - 7 = - 7 Y = - 3 23 + X = -16 To solve this equation for X, you must subtract 23 from both sides. - 23 = - 23 X = - 39 Notice: the sign in front of 23 is positive, so take the opposite

  4. I. Equations with one operation In this equation you are multiplying the variable by 3, therefore perform the opposite operation by dividing both sides by 3 3X = - 27 3 = 3 X = -9 In this equation you are dividing the variable by 24, therefore perform the opposite operation by multiplying both sides by 24 W = 5 24 24 24 W = 120

  5. -6 = -6 W = 31 (-3) (-3) -3 Your Turn! Try These Practice 1 In this equation you are multiplying the variable by -6, therefore perform the opposite operation by dividing both sides by -6 -6X = - 54 X = 9 Practice 2 In this equation you are dividing the variable by -3, therefore perform the opposite operation by multiplying both sides by -3 W = -93

  6. Fraction coefficients What if your variable has a fraction coefficient Example: or One method of solving for the variable is to multiply by the reciprocal of the fraction coefficient

  7. Fraction coefficient equations Note: To multiply a whole number by a fraction, place the whole number over 1 and multiply numerator times numerator and denominator times denominator

  8. Solving Multi-step equations These type of equations involve more than one operation either multiplication or division and addition or subtraction Example 1 Example 2

  9. Solve Example 1 1. Subtract 5 on both sides 2. Divide by 4 on both sides 4 4 Example 2

  10. Solve Example 2 1. Add 3 on both sides 2. Multiply both sides by the reciprocal of the coefficient which is (-5/2)

  11. Answer: Answer: Your Turn! Try these Practice 3 Practice 4

  12. Solving an equation with Variables on Both Sides • Use distributive property to remove parentheses( if any) • Combine like terms on same side of equal sign.(if any) • Get the variable terms on the same side of the equation: Add or subtract to get one of the variable terms to the side of the other variable term with the larger coefficient

  13. Solving an equation with Variables on Both Sides • Move the number term by adding or subtracting • Add If the number term is negative • Subtract if the number term is positive • Move the coefficient by multiplying or dividing • If the coefficient is a fraction, multiply by its reciprocal on both sides

  14. Variable on Both Sides Example

  15. Your Turn! Example

  16. Variable on Both Sides Example

  17. 2W + 2(W+6) = 156 2W + 2W + 12 = 156 W 4W + 12 = 156 -12 = -12 4W = 144 W + 6 4 4 W = 36 Connection: A rectangular garden is fenced on all four sides. If the garden is 6 feet longer than it is wide, what are its dimensions if 156 feet of fencing is needed to enclose it? Let W = width W+6 = length dimensions are 42 feet by 36 feet

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