EXAMPLE 1 Read a problem and make a plan Running

Slides:

Advertisements

Similar presentations

Use the substitution method

Advertisements

Solve an equation by multiplying by a reciprocal

EXAMPLE 1 Standardized Test Practice SOLUTION Substitute several values of h into the equation C = h and solve for C.Then identify the table that.

EXAMPLE 3 Standardized Test Practice SOLUTION

Solve a quadratic system by elimination

Solving Multiplication and Division Equations. EXAMPLE 1 Solving a Multiplication Equation Solve the equation 3x = x = 15 Check 3x = 45 3 (15)

Solve an equation with variables on both sides

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =

EXAMPLE 2 Using the Cross Products Property = 40.8 m Write original proportion. Cross products property Multiply. 6.8m 6.8 = Divide.

Write decimal as percent. Divide each side by 136. Substitute 51 for a and 136 for b. Write percent equation. Find a percent using the percent equation.

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

EXAMPLE 4 Write a circular model Cell Phones A cellular phone tower services a 10 mile radius. You get a flat tire 4 miles east and 9 miles north of the.

Standardized Test Practice EXAMPLE 4 ANSWER The correct answer is B. DCBA Simplify the expression 4(n + 9) – 3(2 + n). 4(n + 9) – 3(2 + n) = Distributive.

Standardized Test Practice

Standardized Test Practice

Standardized Test Practice

3.2 Solving Systems Algebraically

OBJ: To use a problem solving plan to solve problems.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

EXAMPLE 1 Using Mental Math to Solve Equations a. 15 – n = 4 b. 8x = 32 c.r 12 = 4 Solve the equation using mental math.

( ) EXAMPLE 3 Standardized Test Practice SOLUTION 5 x = – 9 – 9

EXAMPLE 2 Rationalize denominators of fractions Simplify

3.1 Solving Equations Algebra I.

Use a Problem Solving Plan

Read a problem and make a plan EXAMPLE 1 Running You run in a city where the short blocks on north-south streets are 0.1 mile long. The long blocks on.

EXAMPLE 3 Write the standard equation of a circle The point (–5, 6) is on a circle with center (–1, 3). Write the standard equation of the circle. SOLUTION.

Copyright © Cengage Learning. All rights reserved. Roots, Radical Expressions, and Radical Equations 8.

1.5 Use a Problem Solving Plan Objective: To be able to use a problem solving plan to solve problems Warm-up: 1.Mr. Lu is planting trees around.

EXAMPLE 1 Using the Commutative Property SOLUTION Write a verbal model to find the total distance you can cycle in 5 days. Tour Biking You are going on.

Using a Commutative Property You are going on a 400 mile bike trip. You plan to cycle at an average speed of 12 miles per hour for 7 hours per day. Can.

1.5 Use a Problem Solving Plan You will use a problem solving plan to solve problems. Essential Question How can you use a problem solving plan to solve.

1. Mr. Lu is planting trees around the perimeter of a rectangular park

Read a problem and make a plan EXAMPLE 1 Running You run in a city where the short blocks on north-south streets are 0.1 mile long. The long blocks on.

Solve an equation by combining like terms EXAMPLE 1 8x – 3x – 10 = 20 Write original equation. 5x – 10 = 20 Combine like terms. 5x – =

Solving by Elimination Example 1: STEP 2: Look for opposite terms. STEP 1: Write both equations in Standard Form to line up like variables. STEP 5: Solve.

Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.

EXAMPLE 1 Solve by equating exponents Rewrite 4 and as powers with base Solve 4 = x 1 2 x – 3 (2 ) = (2 ) 2 x – 3x – 1– 1 2 = 2 2 x– x + 3 2x =

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

EXAMPLE 2 Checking Solutions Tell whether (7, 6) is a solution of x + 3y = 14. – x + 3y = 14 Write original equation ( 6) = 14 – ? Substitute 7 for.

EXAMPLE 1 Solve a two-step equation Solve + 5 = 11. x 2 Write original equation. + 5 = x – 5 = x 2 11 – 5 Subtract 5 from each side. = x 2 6 Simplify.

Use the substitution method

Solve Linear Systems by Substitution January 28, 2014 Pages

(x+2)(x-2).  Objective: Be able to solve equations involving rational expressions.  Strategy: Multiply by the common denominator.  NOTE: BE SURE TO.

Example 3 In parts of New York City, the blocks between streets are called short blocks. There are 20 short blocks per mile. Blocks between avenues are.

Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will.

EXAMPLE 4 Solve linear systems with many or no solutions Solve the linear system. a.x – 2y = 4 3x – 6y = 8 b.4x – 10y = 8 – 14x + 35y = – 28 SOLUTION a.

Solve a two-step equation by combining like terms EXAMPLE 2 Solve 7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide.

Example 1 Read a problem and make a plan

SOLVING SYSTEMS OF EQUATIONS BY SUBSTITUTION PRACTICE PROBLEMS.

Chapter 3 Section 2. EXAMPLE 1 Use the substitution method Solve the system using the substitution method. 2x + 5y = –5 x + 3y = 3 Equation 1 Equation.

Use the elimination method

Warm Up Find the solution to linear system using the substitution method. 1) 2x = 82) x = 3y - 11 x + y = 2 2x – 5y = 33 x + y = 2 2x – 5y = 33.

You Friend EXAMPLE 1 Understanding and Planning

Solve a quadratic system by elimination

1. Add: 5 x2 – 1 + 2x x2 + 5x – 6 ANSWERS 2x2 +7x + 30

EXAMPLE 2 Rationalize denominators of fractions Simplify

( ) EXAMPLE 3 Standardized Test Practice SOLUTION 5 x = – 9 – 9

Solve an equation by multiplying by a reciprocal

Solving One-Step Equations

Solve a system of linear equation in two variables

3.5 Solving systems of equations in 3 variables

Solving Systems of Equations using Substitution

Lesson 1.5 Use a Problem Solving Plan

Solve an equation by combining like terms

Standardized Test Practice

Using Number Sense to Solve One-Step Equations

Example 2B: Solving Linear Systems by Elimination

Solving Equations with Absolute Values

Presentation transcript:

EXAMPLE 1 Read a problem and make a plan Running You run in a city where the short blocks on north-south streets are 0.1 mile long. The long blocks on east-west streets are 0.15 mile long. You will run 2 long blocks east, a number of short blocks south, 2 long blocks west, then back to your starting point. You want to run 2 miles. How many short blocks should you run?

EXAMPLE 1 Read a problem and make a plan SOLUTION STEP 1 Read and Understand What do you know ? You know the length of each size block, the number of long blocks you will run, and the total distance you want to run. You can conclude that you must run an even number of short blocks because you run the same number of short blocks in each direction.

EXAMPLE 1 Read a problem and make a plan What do you want to find out? You want to find out the number of short blocks you should run so that, along with the 4 long blocks, you run 2 miles. STEP 2 Make a Plan Use what you know to write a verbal model that represents what you want to find out. Then write an equation and solve it, as in Example 2.

Solve a problem and look back EXAMPLE 2 Solve a problem and look back Solve the problem in Example 1 by carrying out the plan. Then check your answer. SOLUTION STEP 3 Solve the Problem Write a verbal model. Then write an equation.Let s be the number of short blocks you run. 0.1 s + 0.15 4 = 2 Length of short blocks (miles/block) • Total distance (miles) = Number short blocks (block) + Length of long block (miles/block) Number long blocks (block) The equation is 0.1s + 0.6 = 2. One way to solve the equation is to use the strategy guess, check, and revise.

Solve a problem and look back EXAMPLE 2 Solve a problem and look back Guess an even number that is easily multiplied by 0.1. Try 20. Check whether 20 is a solution. 0.1s + 0.6 = 2 Write equation. 0.1(20) + 0.6 = 2 Substitute 20 for s. 2.6 = 2 Simplify; 20 does not check. Revise. Because 2.6 > 2, try an even number less than 20. Try 14. Check whether 14 is a solution.

Solve a problem and look back EXAMPLE 2 Solve a problem and look back 0.1s + 0.6 = 2 Write equation. 0.1(14) + 0.6 = 2 Substitute 14 for s. 2 = 2 Simplify. ANSWER To run 2 miles, you should run 14 short blocks along with the 4 long blocks you run.

4 EXAMPLE 2 Solve a problem and look back STEP 4 Look Back Check your answer by making a table.You run 0.6 mile on long blocks. Each two short blocks add 0.2 mile. Short blocks 2 4 6 8 10 12 14 Total distance 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 The total distance is 2 miles when you run 4 long blocks and 14 short blocks. The answer in Step 3 is correct.

GUIDED PRACTICE for Examples 2 and 3 WHAT IF? In Example 1, suppose that you want to run a total distance of 3 miles. How many short blocks should you run? ANSWER To run 3 miles, you should run 24 short blocks.