Example 1 Solve ax b c for x. Then use the solution to solve Solve a literal equation + = += 2x 5 11. SOLUTION STEP 1 Solve ax b c for x. += ax b c Write.

Slides:

Advertisements

Similar presentations

Identify the number of solutions of an equation

Advertisements

Do Now 10/15/10 Take out HW from last night.  Textbook p #4-36 even Copy HW in your planner.  Textbook p. 187 #4-30 even  “Pop” Quiz sections.

( ) EXAMPLE 3 Solve ax2 + bx + c = 0 when a = 1

Solving Two-Step Equations

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 Graph direct variation equations Graph the direct variation equation. a.a. y = x 2 3 y = –3x b.b. SOLUTION a.a. Plot a point at the origin. The.

Write reasons for each step

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

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.

Solve a compound inequality with and

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

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. The radius is 3 and the center is at the origin. x 2 + y 2 = r 2 x 2 +

EXAMPLE 3 Solve an equation by factoring Solve 2x 2 + 8x = 0. 2x 2 + 8x = 0 2x(x + 4) = 0 2x = 0 x = 0 or x + 4 = 0 or x = – 4 ANSWER The solutions of.

Standardized Test Practice

Write and graph a direct variation equation

3.2 Solving Systems Algebraically

Subtract b from each side. Write original equation. Solve ax + b = c for x. STEP 1 SOLUTION Solve ax +b = c for x. Then use the solution to solve 2x +

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.

Solve Equations with Variables on Both Sides

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

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

The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

Splash Screen. Example 1 Solve a Logarithmic Equation Answer: x = 16 Original equation Definition of logarithm 8 = 2 3 Power of a Power Solve.

I can solve one-step equations in one variable.. Equations that have the same solutions. In order to solve a one-step equation, you can use the properties.

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.

Literal Equations. ANSWER 2a + 3 = Write an equation for “ 3 more than twice a is 24. ” ANSWER 64 ft 2 2.A square has a side length of 8 feet. Find.

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

Warm Up #4 1. Write 15x2 + 6x = 14x2 – 12 in standard form. ANSWER

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.

Example 1A Solve the equation. Check your answer. (x – 7)(x + 2) = 0

1.6. DEFINITIONS  An equation is a statement that two expressions are equal.  Usually contains 1 or more variables  A variable is a symbol that represents.

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.

Solving Linear Equations Define and use: Linear Equation in one variable, Solution types, Equivalent Equations.

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.

Solving Linear Equations Substitution. Find the common solution for the system y = 3x + 1 y = x + 5 There are 4 steps to this process Step 1:Substitute.

Use the discriminant EXAMPLE 1 Number of solutions Equation ax 2 + bx + c = 0 Discriminant b 2 – 4ac a. x 2 + 1= 0 b. x 2 – 7 = 0 c. 4x 2 – 12x + 9 = 0.

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.

Use the substitution method

Slide Copyright © 2009 Pearson Education, Inc. 6.9 Continued Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula.

Solve Linear Systems by Substitution January 28, 2014 Pages

Solve using mental math.

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.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. SOLUTION The radius is 3 and the center is at the origin. x 2 + y 2 = r.

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

Rewrite a linear equation

7.3 Solving Equations Using Quadratic Techniques

EXAMPLE 2 Rationalize denominators of fractions Simplify

Solve a literal equation

Solving Two-Step Equations

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

Solve an equation by multiplying by a reciprocal

Solve a quadratic equation

Solving Systems of Equations using Substitution

Solve an equation by combining like terms

2 Understanding Variables and Solving Equations.

EXAMPLE 4 Standardized Test Practice SOLUTION

Solving One and Two Step Equations

Standardized Test Practice

Solve an inequality using subtraction

Warm Up #4 1. Write 15x2 + 6x = 14x2 – 12 in standard form. ANSWER

Definition of logarithm

Presentation transcript:

Example 1 Solve ax b c for x. Then use the solution to solve Solve a literal equation + = += 2x SOLUTION STEP 1 Solve ax b c for x. += ax b c Write original equation. + = = bc a – x Assume a 0. Division property of equality = Subtraction property of equality ax– = c b

Example 1 Solve a literal equation STEP 2 Use the solution to solve 2x = Solution of literal equation = bc a – x 3= Simplify. Substitute 2 for a, 5 for b, and 11 for c. = – ANSWER The solution of 2x 5 11 is 3. +=

Guided Practice for Example 1 Solve the literal equation for x. Then use the solution to solve the specific equation. 1. a bx c ; 12 5x 3 – – = – = 2. ax bx c ; 11x 6x 20 =+= + ANSWER = ca b – x ; 3; 3 = ba c x – ; 4; 4