2 Warm Up in Spiral. Solve. 1. x – 16 = 8 2. 7a = 35 3. x = 24 4. y + 21 = 31x = 24a = 5x12x = 132= 11y = 10
3 AF1.1 Write and solve one-step linear equations in one variable. Also covered: NS2.1, NS2.2, NS2.4CaliforniaStandards
4 The 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.
5 Additional 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.
6 Additional 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.
7 Additional 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.
8 Additional 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
9 Solve. 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.
11 Check It Out! Example 1B Continued 438+ y =Substitute for y.1814+1 838=?28+13=?Find a common denominator.=38Add.
12 Solve. 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.
13 Additional 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,.
14 Additional 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 =
15 Check It Out! Example 2ASolve. Write the answer in simplest form.3412x=34=12x34Multiply by the reciprocal of .234.4312.43x=Then simplify.123x=
16 Check It Out! Example 2BSolve. Write the answer in simplest form.673y =673y =Multiply by the reciprocal of 3.2y1367133=Then simplify.127y =
17 Additional 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.
18 Check 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.
19 Solve. Write each answer in simplest form. 1. 2. 3. 4. Lesson QuizSolve. Write each answer in simplest form.22.214.171.124.3858x –=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