Solving equations with Rational Coefficients

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Presentation transcript:

Solving equations with Rational Coefficients mathematical sentence formed by placing an “=“ between two expressions Remember this??? y – 8 = 12 22 = 14 + z 5 ÷ x = 30 11a = 121

Equation Remember this??? x + 7 = 10 Left side Right side ‘x’ has to be 3 in order to make the equation balanced. Like a scale, the left side and right side must be the same in order to be balanced!

Equation 4 7 x = 10 Right side Left side Like a scale, the left side and right side must be the same in order to be balanced!

Objective SWBAT use multiplicative inverses to solve equations with rational coefficients. Coefficient is the numerical factor of a term that contains a variable 18x + 4 = 360 ¾ x = 18 3.15 = 0.45n

Section 5.6, “Using Multiplicative Inverses to Solve Equations” Multiplicative Inverse Property To solve an equation that has a fractional coefficient, you can multiply each side of the equation by the fraction’s multiplicative inverse. MULTIPLICATIVE INVERSE = RECIPROCAL

MULTIPLICATIVE INVERSE– the product of a number and its multiplicative inverse is 1.

Solve for x. -3 1 Multiply each side of the equation by the MULTIPLICATIVE INVERSE of 4/7 Multiply -3 Divide (cancel) common factors 1

Try It Out!! Solve

Solve equations with decimal coefficients To solve an equation with a decimal coefficient, divide each side of the equation by the coefficient 3.15 = .45n 3.15 = .45n Division property of equality .45 .45 7 = n Simplify

Solving Multi-Step Equations Remember this??? Solving Multi-Step Equations How can you get the “unknown” by itself? Solving Equations with Variables on Both Sides STEP 1- Use distributive property and combine like terms. STEP 2- Collect variables on one side of the equation. STEP 3- “Undo” addition and/or subtraction. STEP 4- “Undo” multiplication and/or division. STEP 5- Solve for the variable. STEP 6- Check your work.

Solve for x. -1 1 Subtract 4/5 from each side. Write fractions using LCD Multiply each side of the equation by the MULTIPLICATIVE INVERSE of -7/15 -1 Multiply Divide (cancel) common factors 1

Try It Out!! Solve

Homework Text page 249, #12-32 evens