1.3 Day 2 Solving Eq. with Variables on both Sides

Solving Equations with
Variables on Both Sides

1.3 Day 2

Learning Target

Student will be able to…

●Solve linear equations that have variables on both sides.

●Identify special solutions of linear equations.

●Use linear equations to solve real-life problems.

Multiple Choice

Simplify: $$3\left(g-3\right)$$

• $$3g-9$$

• $$-9g+3$$

• $$3g+9$$

Multiple Choice

Simplify: $$15-2x-3x$$

• $$15-5x$$

• $$-5x-15$$

• $$-15+5x$$

• $$15-x$$

Multiple Choice

Simplify: $$5\left(1+2m\right)-10$$

• $$10m+5$$

• $$-10m-5$$

• $$10m-5$$

• $$-10m+15$$

Special Solutions of Linear Equations

1.One solution–an equation that has only one value of the variables.

2.Identity–an equation that is true for all values of the variables and it has infinitely many solutions.

3.No Solution–equation that is not true for any value of the variables.

Example 1: Identify the Number of Solutions

a)3(5x+2)=15x

b) -2(4y+1)=-8y-2

Example 2

A number is divided by 4, and the quotient is added to 3. The result is 24. What is the number?

Example 3: Real-Life Application

A boat travels x miles per hour from Miami to Nassau. The boat travels 3 miles per hour slower
on the return trip. What is the distance from Miami to Nassau? The speed or rate of the boat
on the return trip is (x-3) miles per hour.

Multiple Choice

Solve: $$-5x-10=2-(x+4)$$

• $$2$$

• $$-2$$

• $$3$$

• $$-3$$