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Additional info for CSET Foundational-Level Mathematics 110, 111 (XAM CSET)
Negative numbers bring us closer to a solution and true statement: Any equation = x + a b, where a, b ∈ Z, has a solution, x ∈ Z, so that the equation has a solution even if the variables or their coefficients are negative. FOUNDATION LEV. MATH. 45 TEACHER CERTIFICATION STUDY GUIDE Example: Other equations over I: 4x - 8 = 0. x = 8/4 = 2. However, 4x + 32 = 0. x = -32/4 = -8, and 3x - 13 = 0. x = 13/3 = what?. Is there an integer that when multiplied by 3 yields 13? No, I is not algebraically closed either.
If there are variables on both sides of the equation, add or subtract one of those variable terms to move it to the other side. Combine like terms. STEP 6. If there are constants on both sides, add or subtract one or more of those constants to both sides. Combine like terms. FOUNDATION LEV. MATH. 17 TEACHER CERTIFICATION STUDY GUIDE STEP 7. If there is a coefficient in front of the variable, divide both sides by this number to get the answer to the equation. However, remember: Dividing or multiplying an inequality by a negative number will reverse the direction of the inequality sign.
Mr. Ziffel bought 3 cows and 12 sheep for $2400. If all the cows were the same price and all the sheep were another price, find the price charged for a cow or for a sheep. Let x = price of a cow Let y = price of a sheep Then Farmer Greenjeans' equation would be: 4 x + 6 y = 1700 Mr. Ziffel's equation would be: 3 x + 12y = 2400 To solve by addition-subtraction: − 2(4 x + 6 y = 1700) Multiply the first equation by − 2 : Keep the other equation the same : (3 x + 12y = 2400) By doing this, the equations can be added to each other to eliminate one variable and solve for the other variable.