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Equations Quiz Remediation/Recovery Directions: The following section illustrates an example of each problem you need to master for this quiz. Following the example is a written explanation of how the problem was solved. In each equation, remember the object is to get “x” alone. Example Variable Step 1: Constant x – 5 = 12 + 5 +5 x = 17 This means divide! Step 1: x = 3 2 (2) x = 3(2) 2 x = 6 This means multiply! Step 1: Step 2: -3x + 8 = 29 -8 -8 -3x = 21 -3 -3 x = -7 A number attached to a parenthesis means you multiply that number times each thing inside the parenthesis! 6 (2x + 3) = 78 Step 1: Step 2: Step 3; 6 (2x + 3) = 6(2x) + 6(3) = 12x + 18 = -18 12x = 12 x = 78 78 78 -18 60 12 5 Explanation of the Steps Step 1: This problem only has one step because in order to get “x” (the variable) alone you only need to get rid of the constant which in this case is negative because it is subtracted from the variable. This means you will add 5 to both sides to get “x” alone. The answer is x = 17. Step 1: This problem only has one step as well. On the left, “x” is being divided by 2. This means we will need to do the inverse operation of division to get rid of the 2, which is multiplication. So we multiply each side by 2 to get “x” alone. The answer is x = 6. Step 1: In this step you MUST first get rid of the constant by subtracting it on both side of the equation. The 8 is subtracted because it added in the equation. This leaves -3x = 21. Step 2: In the step the only thing left is the 3 attached to the x. The -3x means the -3 is multiplied to the x. The inverse of multiplication is division so we have to divide each side by -3. The “x” is now alone. The answer is x = -7. The answer is negative because a positive divided by a negative is a negative. Step 1: In step one you MUST first distribute because you need to follow your order of operations and parenthesis comes first. Distribute means to multiply each term in the parenthesis by 6. This gives you 12x + 18 = 78. Step 2: Next you MUST get rid of the constant. To do this you subtract 18 on both sides of the equation. This gives you 12x = 60. Step 3: Finally you MUST get rid of the 12 in front of the x. To do this you must divide because 12x means 12 times x. The final answer is x = 5. Example Before you can begin to get “x” alone, you must COMBINE LIKE TERMS! Always circle or box your like terms to make it easier to see! - x - 6 - 7x + 20 = -2 Step 1: - x - 6 - 7x + 20 = -2 Step 2: Step 3: -8x + 14 = -14 -8x = -8 x = -2 -14 -16 -8 2 Explanation Step 1: First you must combine like terms! In this equation you must combine the –x and -7x, then you must combine the constants -6 and 20. It gives you -8x + 14 = -2. Step 2: In this step you must get rid of the constant (14). To do this you must subtract 14 from both sides of the equation. This gives you 8x = -16. Step 3: In this step you must get rid of the -8 attached to the x. To do this you, you divide by -8. This gives you the answer x = 2 because a negative divided by an negative is positive.