Warm-Up Exercises 1. 2m – 6 + 4m = 12 ANSWER 6 Solve the equation. 2.6a – 5(a – 1) = 11 ANSWER 3.

Slides:

Advertisements

Similar presentations

Solving Two-Step Equations

Advertisements

Solve an equation with variables on both sides

Solve an equation by combining like terms

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 =

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.

Standardized Test Practice

EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by x2x.

Standardized Test Practice

Standardized Test Practice

Solve a radical equation

5.6 Solve Absolute Value Inequalities

Solve Equations with Variables on Both Sides

Solve Equations With Variables on Both Sides

2.5 Solve Equations with variables on Both Sides

Solving Two-Step Equations You will solve equations by undoing operations using properties of equality. Essential Question: How do you solve two-step equations?

EXAMPLE 2 Rationalize denominators of fractions Simplify

EXAMPLE 1 Solve an equation with variables on both sides 7 – 8x = 4x – 17 7 – 8x + 8x = 4x – x 7 = 12x – = 12x Write original equation. Add.

2.5 Solving equations with variables on both sides

Solving Equations Medina1 Variables on Both Sides.

1-8 Solving Equations by Adding or Subtracting Warm-up: Fluency Quiz. Sit with paper blank side up. Homework: Page 41 #4-8 even, #12-16 even, even,

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

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

5.3: Solving Addition Equations Goal #1: Solving Addition Problems Goal #2: Writing Addition Equations.

Solve a two-step inequality EXAMPLE 1 3x – 7 < 8 Write original inequality. 3x < 15 Add 7 to each side. x < 5 Divide each side by 3. ANSWER The solutions.

Writing and Solving a Two-Step Equation EXAMPLE 2 The sum of 4 times a number plus –6 is 14. What is the number? 4 times a number and –6 is 14. Write a.

Solve Multi-Step Equations

2.4 Solve Multi-Step Equations

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

1. solve equations with variables on both sides. 2. solve equations containing grouping symbols. Objectives The student will be able to:

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.

Systems of Equations: Substitution

Use the substitution method

Solve Linear Systems by Substitution January 28, 2014 Pages

5.5 Solve Absolute Value Equations

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

2.3 Solve two-step equations You will solve two-step equations Essential question: How do you solve two-step equations?

Graphing Linear Inequalities 6.1 & & 6.2 Students will be able to graph linear inequalities with one variable. Check whether the given number.

Notes 3.4 – SOLVING MULTI-STEP INEQUALITIES

Warm-Up Discuss your solutions with your neighbor Give an example of Distributive Property Simplify the following expression -2(3x – 5) -6x + 10 ** Be.

6-2 Solving Systems Using Substitution Hubarth Algebra.

3-3 HW: Pg #4-16eoe, 18-28e, 38,

Solving Equations with Variables on Both Sides. Review O Suppose you want to solve -4m m = -3 What would you do as your first step? Explain.

LAB: Inequalities with Negative Coefficients p.304 Q U E ST ION: How do you solve an inequality with a negative coefficient?

3.5 Solving Equations with Variables on Both Sides.

Solving Linear Systems Using Substitution There are two methods of solving a system of equations algebraically: Elimination Substitution - usually used.

Solve the equation. 1. = 4 x x(x – 4) = 3(x – 4) + x ANSWER 10

Substitution Method: Solve the linear system. Y = 3x + 2 Equation 1 x + 2y=11 Equation 2.

Rewrite a linear equation

Objectives The student will be able to:

Example: Solve the equation. Multiply both sides by 5. Simplify both sides. Add –3y to both sides. Simplify both sides. Add –30 to both sides. Simplify.

EXAMPLE 2 Rationalize denominators of fractions Simplify

Solving Equations with the Variable on Each Side

Solving Equations with Variables on Both Sides 1-5

Solve a literal equation

Solve for variable 3x = 6 7x = -21

Solve an equation by multiplying by a reciprocal

Solve a quadratic equation

6-2 Solving Systems By Using Substitution

6-2 Solving Systems Using Substitution

Solving Systems using Substitution

Objectives The student will be able to:

Solve an equation by combining like terms

Equations: Multi-Step Examples ..

Objectives Solve systems of linear equations in two variables by elimination. Compare and choose an appropriate method for solving systems of linear equations.

Solving Multi-Step Equations

Solve an inequality using subtraction

2-5 Solving Equations with the Variable on Each Side

Presentation transcript:

Warm-Up Exercises 1. 2m – 6 + 4m = 12 ANSWER 6 Solve the equation. 2.6a – 5(a – 1) = 11 ANSWER 3

Warm-Up Exercises 3. A charter bus company charges $11.25 per ticket plus a handling charge of $.50 per ticket, and a $15 fee for booking the bus. If a group pays $297 to charter a bus, how many tickets did they buy? ANSWER 24 tickets Solve the equation.

Warm-Up Exercises EXAMPLE 1 Solve an equation with variables on both sides 7 – 8x = 4x – 17 7 – 8x + 8x = 4x – x 7 = 12x – = 12x Write original equation. Add 8x to each side. Simplify each side. Add 17 to each side. Divide each side by 12. ANSWER The solution is 2. Check by substituting 2 for x in the original equation. Solve 7 – 8x = 4x – = x

Warm-Up Exercises EXAMPLE 1 Solve an equation with variables on both sides Write original equation. Substitute 2 for x. Simplify left side. Simplify right side. Solution checks. –9 = 4(2) – 17 ? 7 – 8(2) = 4(2) – 17 ? 7 – 8x = 4x – 17 CHECK –9 = –9

Warm-Up Exercises EXAMPLE 2 Solve an equation with grouping symbols 1 4 (16x + 60) 9x – 5 = 9x – 5 = 4x x – 5 = 15 5x = 20 x = 4 Write original equation. Distributive property Subtract 4x from each side. Add 5 to each side. Divide each side by 5. 9x – 5 =9x – 5 = 1 4 (16x + 60). Solve

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and c = 4c – 7 ANSWER 9 Solve the equation. Check your solution.

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and – 3k = 17k – 2k Solve the equation. Check your solution. ANSWER –8

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and z – 2 = 5+3(3z – 4) Solve the equation. Check your solution. ANSWER

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and – 4a = 5(a – 3) Solve the equation. Check your solution. ANSWER 2

Warm-Up Exercises GUIDED PRACTICE for Example z + 12 = 9(z + 3) Solve the equation, if possible. ANSWER no solution

Warm-Up Exercises GUIDED PRACTICE for Example w + 1 = 8w + 1 ANSWER 0 Solve the equation, if possible.

Warm-Up Exercises GUIDED PRACTICE for Example (2a + 2) = 2(3a + 3) ANSWER identity Solve the equation, if possible.

Warm-Up Exercises Daily Homework Quiz Solve the equation, if possible. 3(3x + 6) = 9(x + 2)1. 7(h – 4) = 2h ANSWERThe equation is an identity. ANSWER 9 8 – 2w = 6w – 83. ANSWER 2

Warm-Up Exercises Daily Homework Quiz 4g + 3 = 2(2g + 3)4. ANSWERThe equation has no solution. ANSWER 5 h Bryson is looking for a repair service for general household maintenance. One service charges $75 to join the service and $30 per hour. Another service charge $45 per hour. After how many hours of service is the total cost for the two services the same ? 5.