Solve Equations with Variables on Both Sides

Slides:

Advertisements

Similar presentations

Identify the number of solutions of an equation

Advertisements

3-5 Solving Equations with the variable on each side Objective: Students will solve equations with the variable on each side and equations with grouping.

Solve an equation with variables on both sides

Solve an equation by combining like terms

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

Lesson 2-4. Many equations contain variables on each side. To solve these equations, FIRST use addition and subtraction to write an equivalent equation.

Step 1: Simplify Both Sides, if possible Distribute Combine like terms Step 2: Move the variable to one side Add or Subtract Like Term Step 3: Solve for.

Solving Equations with Variables on Both Sides

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

Introduction Two equations that are solved together are called systems of equations. The solution to a system of equations is the point or points that.

Standardized Test Practice

An equation is a mathematical statement that two expressions are equivalent. The solution set of an equation is the value or values of the variable that.

1. solve equations with variables on both sides. 2. solve equations containing grouping symbols. 3.5 Objectives The student will be able to:

2.5 Solve Equations with variables on Both Sides

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.

1.4 Solving Equations ●A variable is a letter which represents an unknown number. Any letter can be used as a variable. ●An algebraic expression contains.

3-2 Solving Equations by Using Addition and Subtraction Objective: Students will be able to solve equations by using addition and subtraction.

2.5 Solving equations with variables on both sides

Solving Equations Medina1 Variables on Both Sides.

Example 1 Solve an Equation with Variables on Each Side Solve 8 + 5c = 7c – 2. Check your solution c = 7c – 2Original equation Answer: c = 5Simplify.

Martin-Gay, Beginning Algebra, 5ed Using Both Properties Divide both sides by 3. Example: 3z – 1 = 26 3z = 27 Simplify both sides. z = 9 Simplify.

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

Algebra 1 Chapter 3 Section Solving Inequalities With Variables on Both Sides Some inequalities have variable terms on both sides of the inequality.

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.

Solve Multi-Step Equations

§ 2.2 The Addition Property of Equality. Angel, Elementary Algebra, 7ed 2 Linear Equations A linear equation in one variable is an equation that can be.

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.

1.4 Solving Multi-Step Equations. To isolate the variable, perform the inverse or opposite of every operation in the equation on both sides of the equation.

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

Use the substitution method

Solve Linear Systems by Substitution January 28, 2014 Pages

1. solve equations with variables on both sides. 2. solve equations with either infinite solutions or no solution Objectives The student will be able to:

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

Solve 7n – 2 = 5n + 6. Example 1: Solving Equations with Variables on Both Sides To collect the variable terms on one side, subtract 5n from both sides.

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

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

Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Homework # 10 – Word Problems pg 152 # 40 To qualify for a lifeguard training course, you.

§ 2.3 Solving Linear Equations. Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 Solving Linear Equations Solving Linear Equations in One Variable.

Rewrite a linear equation

Objectives The student will be able to:

6-3: Solving Equations with variables on both sides of the equal sign

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.

Solving Equations with the Variable on Each Side

Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.

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

2 Understanding Variables and Solving Equations.

Solve a quadratic equation

Objectives The student will be able to:

Objectives The student will be able to:

Objective Solve equations in one variable that contain variable terms on both sides.

Solve an equation by combining like terms

1.3 Solving Linear Equations

Solving Multi-Step Equations

Solving One and Two Step Equations

Objective Solve equations in one variable that contain variable terms on both sides.

Solve an inequality using subtraction

Section Solving Linear Systems Algebraically

Objectives The student will be able to:

Algebra 1 09/21/16 EQ: How do I solve equations with variables on both sides? HW: Due Friday pg. 95 # 1-33 all Bring textbooks tomorrow Quiz on Friday.

Objectives The student will be able to:

2-3 Equations With Variables on Both Sides

2-5 Solving Equations with the Variable on Each Side

Objectives The student will be able to:

Skill Check Lesson Presentation Lesson Quiz.

Presentation transcript:

Solve Equations with Variables on Both Sides Chapter 2.5 Solve Equations with Variables on Both Sides

Key Concept Some equations have variables on both sides. To solve such equations, you can collect the variable terms on one side of the equation and the constant terms on the other side of the equation.

Solve an equation with variables on both sides EXAMPLE 1 Solve an equation with variables on both sides Solve 7 – 8x = 4x – 17. 7 – 8x = 4x – 17 Write original equation. 7 – 8x + 8x = 4x – 17 + 8x Add 8x to each side. 7 = 12x – 17 Simplify each side. 24 = 12x Add 17 to each side. 2 = x Divide each side by 12. ANSWER The solution is 2. Check by substituting 2 for x in the original equation.

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

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

On Your Own GUIDED PRACTICE Solve the equation. Check your solution. 1. 24 – 3m = 5m 3 ANSWER

On Your Own GUIDED PRACTICE Solve the equation. Check your solution. 2. 20 + c = 4c – 7 ANSWER 9

On Your Own GUIDED PRACTICE Solve the equation. Check your solution. 3. 9 – 3k = 17k – 2k ANSWER –8

On Your Own GUIDED PRACTICE Solve the equation. Check your solution. 4. 5z – 2 = 2(3z – 4) ANSWER 6

On Your Own GUIDED PRACTICE Solve the equation. Check your solution. 5. 3 – 4a = 5(a – 3) ANSWER 2

On Your Own GUIDED PRACTICE Solve the equation. Check your solution. 2 3 (6y + 15) 6. ANSWER 4

NUMBER OF SOLUTIONS Equations do not always have one solution. An equation that is true for all values of the variable is an identity . So, the solution of an identity is all real numbers. Some equations have no solution.

Identify the number of solutions of an equation EXAMPLE 4 Identify the number of solutions of an equation Solve the equation, if possible. a. 3x = 3(x + 4) b. 2x + 10 = 2(x + 5) SOLUTION a. 3x = 3(x + 4) Original equation 3x = 3x + 12 Distributive property The equation 3x = 3x + 12 is not true because the number 3x cannot be equal to 12 more than itself. So, the equation has no solution. This can be demonstrated by continuing to solve the equation.

Identify the number of solutions of an equation EXAMPLE 4 3x – 3x = 3x + 12 – 3x Subtract 3x from each side. 0 = 12 Simplify. ANSWER The statement 0 = 12 is not true, so the equation has no solution.

Identify the number of solutions of an equation EXAMPLE 1 EXAMPLE 4 Identify the number of solutions of an equation b. 2x + 10 = 2(x + 5) Original equation 2x + 10 = 2x + 10 Distributive property ANSWER Notice that the statement 2x + 10 = 2x + 10 is true for all values of x. So, the equation is an identity, and the solution is all real numbers.

On Your Own GUIDED PRACTICE Solve the equation, if possible. 8. 9z + 12 = 9(z + 3) ANSWER no solution

On Your Own GUIDED PRACTICE Solve the equation, if possible. 9. 7w + 1 = 8w + 1 ANSWER

On Your Own GUIDED PRACTICE Solve the equation, if possible. 10. 3(2a + 2) = 2(3a + 3) ANSWER identity