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Extra info for CSET Foundational-Level Mathematics 110, 111 (XAM CSET)
This will cancel out all of the fractions making it easier to solve the equation or inequality. STEP 3. If there are decimals, find the largest decimal. ) with the same number of zeros as the length of the decimal. This will eliminate all decimals while solving the equation or inequality. STEP 4. Combine like terms on each side of the equation or inequality. STEP 5. 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.
Graph the parabola as a dotted line if the inequality sign is either < or > . Graph the parabola as a dotted line if the inequality sign is either ≤ or ≥ . Shade above (or inside) the parabola if the sign is ≥ or > . Shade below (or outside) the parabola if the sign is ≤ or < . Example: Solve: 8 x 2 − 10 x − 3 = 0 In this equation a = 8 , b = −10 , and c = − 3 . Substituting these into the quadratic equation, it becomes: x = = x − − ( 10) ± ( −10)2 − 4(8)( − 3) 10 ± 100 − 96 = 2(8) 16 10 ± 196 10 ± 14 = = 24 = 16 3 2 or −= 4 16 16 16 FOUNDATION LEV.
23 TEACHER CERTIFICATION STUDY GUIDE 60 x + 75 y ≥ 300 solves to y ≥ 4 − 4 5 x 75y + 60x ≥ 300 75y ≥ −60x + 300 4 y ≥ − x+4 5 Example: Graph these 2 inequalities: y ≤ 8 −1 2 x y ≥ 4−4 5x Daily Production of Bikes Sold 9 Number of 10 Speed Bikes Sold 8 y ≤8− 7 1 x 2 6 5 4 y ≥ 4− 3 2 4 x 5 1 0 0 5 10 15 20 Number of 3 Speed Bikes Sold Realize that x ≥ 0 and y ≥ 0 , since the number of bikes assembled cannot be a negative number. Graph these as additional constraints on the problem. The number of bikes assembled must always be an integer value, so points within the shaded area of the graph must have integer values.