34 + After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. + y 19 Begin by translating the sentence into an equation. c ) q The trip will cost him $525 for airfare, $780 for food and sightseeing, and $95 per night for the hotel. + Notice that we want to add two quantities: one unknown number and the number 4. such solutions is the solution set of the inequality. indicate that a number is not part of the graph. 4 Solve: 4(a3)7=25.4(a3)7=25. <<5954435D46DFB44AB6A74445E5396B31>]>>
In the following exercises, translate to an equation and then solve. The algebraic expressions in this section may contain two or more operations. Cesar is planning a four-day trip to visit his friend at a college in another state. 35, 6 18 7 9 Example 4: Write an algebraic expression for the math phrase a number less than 8. + How many invitations must she write to earn a profit of at least $2,800 per month? ( 5 46 Using the letter k as the variable, we can translate the statement above as 10 + k. Since addition is commutative, we can rewrite it as k + 10. ) Solve: 6(r2)12=30.6(r2)12=30. 4 20, In the next example, we will find the number of jobs a small businesswoman needs to do every month in order to make a certain amount of profit. This website uses cookies to ensure you get the best experience on our website. 15 2 The three main components of algebraic expressions are numbers, variables, and arithmetic operations. Add the numbers in the columns using long addition + the number of text messages Taleisha can make. Solution: Suppose the variable y is the unknown number. Is this the appropriate phone plan for you? = p Example 1: Write an algebraic expression for the math phrase 3 more than twice a number. How many children will she put in each group? Graph each inequality on the number line and write in interval notation: x4x4 x0.5x0.5 x<23.x<23. 12 = 3x: Half of a number is twenty. To solve your inequality using the Inequality Calculator, type in your inequality like x+7>9. 46 For any numbers a, b, and c, and c0c0. 19 How many lawns must he mow to have enough money to pay for the trip? b Multiply the tens digit in the bottom number by each digit in the top number. OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. The restaurant charges $350 for the banquet room plus $32.50 per person for lunch. If you think about it, there is an unknown number represented by variable x that is being doubled or multiplied by 2. 4 3, 12 x ) ) = + Example 2 We are not done yet. Suppose the unknown number is t, we get. 1 ) 72, 6 . 6 In set-builder notation, the solution set is {y|y>=3/5}, while in interval Solution: The word difference suggests that we are going to subtract. 5 y 10 They plan to rent a car from a company that charges $75 a week plus $0.25 a mile. p If you need help with long addition see our k ( He has $840 in savings, and he earns $45 per hour for tutoring. 0, reverse the direction of the inequality symbol. trailer
= Solve Applications with Linear Inequalities. 4 The cost is $9850 for up to 100 guests, plus $38 for each additional guest. How many miles can they travel during the week and still keep within their $200 budget? 9 Figure 2.2 shows both the number line and the interval notation. How do you translate the following statement "The product of five less than a number and two is six" into an algebraic expression and then find the number? We write x1x1 in interval notation as (,1].(,1]. The key is to recognize that we are going to add a quotient and a product. 6.30. h + When multiplying or dividing both sides of an inequality by a negative Please ensure that your password is at least 8 characters and contains each of the following: You'll be able to enter math problems once our session is over. 6 v 1 u 18 Many real-life situations require us to solve inequalities. 2 It costs him $10.55 for a bucket of balls each time he goes. 12 1 In addition, when you encounter this math word (difference) make sure to pay attention to the order. Solve the equation 0.49s+0.21(s5)=9.450.49s+0.21(s5)=9.45 for s, to find the number of 49-cent stamps Travis bought. Translate and solve: nn divided by 7 is equal to 2121. 2 In the following exercises, graph each inequality on the number line and write in interval notation. 2 " 2 2 more than 5 5 ". We will need to raise the unknown number by 2 then divide it by 3. 9 A linear inequality is much like a linear equationbut the equal sign is replaced with an inequality sign. write the 1 and carry 1 To translate English sentences into inequalities, we need to recognize the phrases that indicate the inequality. She expects to pay $350 airfare, $375 for food and entertainment and $60 a night for her share of a hotel room. Selecting the lettermas our variable, the algebraic expression for this math phrase is simply5m. How many hours must she babysit to have enough money to pay for the trip? 4 Solution: Be very careful when dealing with the keywords less than. a They can earn the rest of the money they need by having a car wash. 1 y h 5 Carry the 1 to the Hundreds place. q While the quantity that comes after it becomes the minuend. When you add, subtract, multiply, or divide the same quantity from both sides of an equation, you still have equality. Learn to write algebraic expressions in and out of word problems. Shower budget Penny is planning a baby shower for her daughter-in-law. 5 = The notation for inequalities on a number line and in interval notation use the same symbols to express the endpoints of intervals. Find your last months phone bill and the hourly salary you are paid at your job. Other Math questions and answers. q Two numbers when multiplied equals 42. 7 Add the 2 that you carried = 17 14 16 z He has $189 in savings and can earn $35 for each lawn he mows. = u ), 4 4 ) x We can show 2 Police Incident In Burscough Today,
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