![]() The class expands on the concepts of equations, functions, and graphs previously introduced in the prerequisite course, Algebra I. ![]() Then, isolate the variable and solve for x.Students typically take Algebra II early in their high school careers. First, simplify the left side of the equation. Therefore, someone can travel 13 miles on $12.ġ0. To find how far someone can travel with $12, substitute 12 for C and solve for D. Because the first half-mile is excluded, ½, or 0.5 must be subtracted from the distance when multiplying by 0.70. If one travels more than half a mile, the cost is $3.25 plus the $0.70 times the distance in miles, excluding the first half-mile. To begin, write an equation relating the cost C to the distance D. To find Carol’s age, multiply Andrew’s age by three. ![]() Since the first two equations are already solved for C and B, substitute the expressions on the right side into the third equation. Write each piece of information as an equation using the variables A, B, and C for the current ages of Andrew, Brad, and Carol, respectively. The result is the inequality 9 < x < 121.Ĩ. To find the value of x, square each part of the inequality. Since the square root of x is between 3 and 11, we know that the inequality 3ġ1 is true. For a fraction, the reciprocal can be found by inverting (or switching) the numerator and denominator. The product of a number and its reciprocal, or multiplicative inverse, is 1. Next, substitute 7 for x in the expression 5x + 23 and simplify the result.Ħ. To begin, solve the given equation for x. In order to make the equation true, the expression inside the absolute value, x + 5, can equal either -3 or 3 since the absolute value of both values is 3. Since distances are never negative, the absolute value of a number is always positive (or equal to zero). The absolute value of a number is its distance from zero on a number line. This equation involves an absolute value function. Then, solve the equation by isolating the variable and dividing both sides by the coefficient.Ĥ. To begin, simplify the right side of the equation by distributing the 3. Then, simplify the result and solve for x.ģ. Form a new equation by multiplying the numerator of each fraction by the denominator of the fraction on the other side. This equation is a proportion, so it can be solved by cross-multiplication. Therefore, the salesman sold $50,000 worth of steak knives last year.Ģ. Solve the equation for x by dividing both sides by 1.2. Since the salesman’s sales increased by 20% since last year’s, his current sales 120% of x, or 1.2x. Let x represent the total value of last year’s sales, Set up an equation and solve it for x. A cab ride costs $3.25 for the first half-mile and $0.70 for each mile after the first half-mile. In six years, the sum of Andrew’s and Brad’s ages will be the same as Carol’s age. If the positive square root of x is between 3 and 11, then what inequality represents all possible values of x?Ĩ. What was the value of his sales last year?ĥ. This represents a 20% increase from the year before. This year, a salesman sells a total of $60,000 worth of steak knives by going door-to-door.
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