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.

Slides:

Advertisements

Similar presentations

Identify the number of solutions of an equation

Advertisements

2.6 Factor x2 + bx + c.

Do Now Pass out calculators. Work on practice EOC Week # 8.

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.

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

Solve an equation with variables on both sides

EXAMPLE 1 Solve a quadratic equation by finding square roots Solve x 2 – 8x + 16 = 25. x 2 – 8x + 16 = 25 Write original equation. (x – 4) 2 = 25 Write.

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 =

EXAMPLE 2 Solve a matrix equation SOLUTION Begin by finding the inverse of A = Solve the matrix equation AX = B for the 2 × 2 matrix X. 2 –7 –1.

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

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

Solve an equation with an extraneous solution

7-5 Logarithmic & Exponential Equations

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

Solve an equation with an extraneous solution

( ) 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

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.

Factor Special Products April 4, 2014 Pages

CAR SALES Solve a real-world problem EXAMPLE 3 A car dealership sold 78 new cars and 67 used cars this year. The number of new cars sold by the dealership.

Solve a logarithmic equation

EXAMPLE 4 Solve a logarithmic equation Solve log (4x – 7) = log (x + 5). 5 5 log (4x – 7) = log (x + 5) x – 7 = x x – 7 = 5 3x = 12 x = 4 Write.

Warm-Up Exercises Factor out a common binomial EXAMPLE 1 2x(x + 4) – 3(x + 4) a. 3y 2 (y – 2) + 5(2 – y) b. Factor – 1 from ( 2 – y ). Distributive property.

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

Factoring to Solve Quadratic Equations

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

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.

Example 3 Solving an Equation Using Addition The solution is ANSWER Original equation 13=4.5c– Add 4.5 to each side. (Addition property of equality)

EXAMPLE 1 Identify slope and y-intercept Identify the slope and y- intercept of the line with the given equation. y = 3x x + y = 22. SOLUTION The.

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

4 = 4 Solve each equation. Check your answers. a. x – 5 = 4 x – 5 = 4

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

Warm – Up # 9 Factor the following: 1.3x 2 – 2x – 5 2.4x x + 25.

CHAPTER 9 LESSON 4 SOLVE POLYNOMIAL EQUATIONS in FACTORED FORM.

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.

Objective  SWBAT solve polynomial equations. Section 9.4 “Solve Polynomial Equations in Factored Form” If ab = 0, then a = 0 or b = 0. The zero-product.

Solve Polynomial Equations in Factored Form March 25, 2014 Pages

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

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

EXAMPLE 2 Rationalize denominators of fractions Simplify

Solve a literal equation

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

Solve an equation by multiplying by a reciprocal

Solve a quadratic equation

Solving Equations by Factoring and Problem Solving

Do Now 1) t + 3 = – 2 2) 18 – 4v = 42.

Solve an equation by combining like terms

EXAMPLE 4 Standardized Test Practice SOLUTION

Example 5A: Solving Simple Rational Equations

3(9z + 4) > 35z – 4 Original problem. Solve each inequality. Then graph the solution set on the number line. 3(9z + 4) > 35z – 4 Original problem.

Objective SWBAT solve polynomial equations in factored form.

Definition of logarithm

EXAMPLE 4 Solve proportions Solve the proportion. ALGEBRA a x 16

Presentation transcript:

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 the equation are 0 and – 4. Solve for x. Zero-product property Factor left side. Write original equation.

EXAMPLE 4 Solve an equation by factoring Solve 6n 2 = 15n. 6n 2 – 15n = 0 3n(2n – 5) = 0 3n = 0 n = 0 2n – 5 = 0 n = 5 2 or Solve for n. Zero-product property Factor left side. Subtract 15n from each side. ANSWER The solutions of the equation are 0 and 5 2.

GUIDED PRACTICE for Examples 3 and 4 Solve the equation. ANSWER 0 and – 5 3. a 2 + 5a = s 2 – 9s = 0 ANSWER 0 and x 2 = 2x. ANSWER 0 and