2Warm Up in Spiral. Solve. 1. x – 16 = 8 2. 7a = 35 3. x = 24 4. y + 21 = 31x = 24a = 5x12x = 132= 11y = 10
3AF1.1 Write and solve one-step linear equations in one variable. Also covered: NS2.1, NS2.2, NS2.4CaliforniaStandards
4The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to get the variable by itself on one side of the equation.
5Additional Example 1A: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form.3757x –=Think: What is happening to x. How do I undo that?x –37=537Since is subtracted from x,add to both sides.x –37+=5x=871Simplify.
6Additional Example 1B: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form.38512+t =38+t=512Since is added to t,38subtract from both sides.38+t–=512t =1024–9Find a common denominator.t =124Subtract.
7Additional Example 1C: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form.4912+ r =49+r12=Since is added to r,49subtract from both sides.49r491249+–=––r =9188Find a common denominator.r =118Subtract.
8Additional Example 1C Continued Check.4912+ r =Substitute for r.11849+1 1812=?818+19=?Find a common denominator.=918Add.You can check that a value is a solution to an equation by substituting the value for the variable. Substitute and solve. Is it correct?Helpful Hint
9Solve. Write the answer in simplest form. Check It Out! Example 1ASolve. Write the answer in simplest form.3878x –=x –38=7Since is subtracted from x, addto both sides.38x –38+=7x =108= 114Simplify.
10+ y = Check It Out! Example 1B Solve. Write the answer in simplest form.1438+ y =14+y=38Since is added to y, subtractfrom both sides.141438+y–=38y=–2Find a common denominator.y=18Subtract.
11Check It Out! Example 1B Continued 438+ y =Substitute for y.1814+1 838=?28+13=?Find a common denominator.=38Add.
12Solve. Write the answer in simplest form. Check It Out! Example 1CSolve. Write the answer in simplest form.31427+t =314+t=27Since is added to t,314subtract from both sides.314+t–=27t =–3144Find a common denominator.t=114Subtract.
13Additional Example 2A: Solving Equations by Multiplying Solve. Write the answer in simplest form.38x=1438=14x38Multiply by the reciprocal of .238831483x=Then simplify.123x=Caution!To undo multiplying by38, you can divide by3883or multiplyby its reciprocal,.
14Additional Example 2B: Solving Equations by Multiplying Solve. Write the answer in simplest form.894y =894y =Multiply by the reciprocal of 4.2141489=Then simplify.4y129y =
15Check It Out! Example 2ASolve. Write the answer in simplest form.3412x=34=12x34Multiply by the reciprocal of .234.4312.43x=Then simplify.123x=
16Check It Out! Example 2BSolve. Write the answer in simplest form.673y =673y =Multiply by the reciprocal of 3.2y1367133=Then simplify.127y =
17Additional Example 3: Physical Science Application The amount of copper in brass is of the total weight. If a sample contains 4 ounces of copper, what is the total weight of the sample?3415Let w represent the total weight of the sample.34w = 415Write an equation.34w 431543= 4Multiply by the reciprocal of34715Write 4as an improperw =21543fraction.1285w =or 535Then simplify.35The sample weighs 5ounces.
18Check It Out! Example 3The amount of copper in zinc is of the total weight. If a sample contains 5 ounces of copper, what is the total weight of the sample?1413Let w represent the total weight of the sample.14w = 53Write an equation.14w 411341= 5Multiply by the reciprocal of1413Write 5as an improperw =16341fraction.643w =or 2113Multiply.13The sample weighs 21ounces.
19Solve. Write each answer in simplest form. 1. 2. 3. 4. Lesson QuizSolve. Write each answer in simplest form.18.104.22.168.3858x –=17161932532y +=x4371275or 1=34131697or 1x=15. Over the course of a week, Marissa ate some apples from a basket on the table. She left 20 apples in the basket. This was five-eighths the number of apples her mother had picked earlier in the week. How many apples did her mother pick?32