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Big Ideas Math: Modeling Real Life, Grade 7 View details

3. Solving Two-Step Equations

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Exercise 31 Page 143

Start by subtracting 45 from both sides.

v= -1/30

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the Properties of Equality. In this case, the only variable term is already on the left-hand side of the equation, so we will start by subtracting 45 from both sides.

- 9/4v+4/5= 7/8

SubEqn

LHS-4/5=RHS-4/5

- 9/4v+4/5-4/5= 7/8-4/5

▼

Subtract term

ExpandFrac

a/b=a * 5/b * 5

- 9/4v+4/5-4/5= 7 * 5/8 * 5-4/5

ExpandFrac

a/b=a * 8/b * 8

- 9/4v+4/5-4/5= 7 * 5/8 * 5-4 * 8/5 * 8

Multiply

- 9/4v+4/5-4/5= 35/40-32/40

SubFrac

Subtract fractions

- 9/4v+4-4/5= 35-32/40

SubTerm

Subtract term

- 9/4v+0/5= 3/40

0/a=0

- 9/4v+0=3/40

IdPropAdd

Identity Property of Addition

- 9/4v= 3/40

Now, we are going to multiply the equation by - 4, and then divide it by 9 using the Multiplication and Division Properties of Equality. This will help us get rid of the fraction. Let's go!

- 9/4v= 3/40

MoveRightFacToNum

a/c* b = a* b/c

- 9v/4= 3/40

MoveNegFracToDenom

Put minus sign in denominator

9v/- 4= 3/40

MultEqn

LHS * (- 4)=RHS* (- 4)

9v/- 4 * (- 4)= 3/40 * (- 4)

FracMultDenomToNumber

a/(- 4)* (- 4) = a