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Glencoe Math: Course 2, Volume 2

GM

Glencoe Math: Course 2, Volume 2 View details

3. Solve Equations with Rational Coefficients

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Exercise 20 Page 463

Multiply both sides of the equation by the reciprocal of 47.

v = 91/6

Practice makes perfect

To solve an equation, we should isolate the variable term. In this case, we will use the Multiplication Property of Equality and multiply both sides of the equation by the reciprocal of 47.

- 4/7v = - 8 23

LHS * (- 1)=RHS* (- 1)

- 4/7v* (- 1) = - 8 23* (- 1)

MultNegNegOnePar

- a(- b)=a* b

4/7v = 8 23

LHS * 7/4=RHS* 7/4

4/7v * 7/4 = 8 23 * 7/4

CommutativePropMult

Commutative Property of Multiplication

4/7 * 7/4* v = 8 23 * 7/4

MultFracByInverse

a/b* b/a=1

v = 8 23 * 7/4

▼

Simplify right-hand side

Write as a sum

v = (8 + 2/3) * 7/4

a = 3* a/3

v = (24/3 + 2/3) * 7/4

Add fractions

v = 26/3* 7/4

Multiply fractions

v = 182/12

a/b=.a /2./.b /2.

v = 91/6

The solution to the equation is v = 916. We can check our solution by substituting it into the original equation.

- 4/7v = - 8 23

v= 91/6

- 4/7* 91/6? =- 8 23

Multiply fractions

- 4* 91/7* 6? =- 8 23

SplitIntoFactors

Split into factors

- 2* 2* 7* 13/7* 2* 3? =- 8 23

CancelCommonFac

Cancel out common factors

- 2* 2* 7* 13/7* 2* 3? =- 8 23

Simplify quotient

- 2* 13/3? =- 8 23

Multiply

- 26/3? =- 8 23

Write as a sum

- 24/3-2/3? =- 8 23

Calculate quotient

- 8 - 2/3? =- 8 23

Subtract term

- 8 23 = - 8 23 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.

Subchapter links

Guided Practice p.460

Independent Practice p.461-462

H.O.T. Problems p.462

Standardized Test Practice p.462-464

Extra Practice p.463

Common Core Review p.464