Download 8.6 Clear Decimals From Two-Step Equations

8.6 Clear Decimals From Two-Step
Equations
Common Core Standards
8. EE.7. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution,
infinitely many solutions, or no solutions. Show which of these
possibilities is the case by successively transforming the given
equation into simpler forms, until an equivalent equation of the form x =
a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including
equations whose solutions require expanding expressions using the
distributive property and collecting like terms.
WARM-UP
Solve the equation.
1) 2x + 10 = 12
Evaluate the expressions.
2) .2 × 10
3) 1× 10
5) Solve the equation.
.2x + 1 = 1.2
4) 1.2 × 10
Clear Decimals From Tw0-Step
Equations
Why do these two equations have the
same answer?
.3x − 1.5 = 4.5
3x − 15 = 45
NOTES
We can clear decimals from any equation by moving
the decimal point the same amount of spaces to the
right in every term to make an equivalent equation.
Examples
Clear the decimals from the equations.
.2x + .6 = 3
.03x + .2 = .11
NOTES
This works because as long as you multiply both sides
of an equation by the same amount, it remains
equivalent and has the same answer.
Examples
Multiply both sides of the equation by 10, 100, or 1000
to clear the decimals from the equations.
.09x + .5 = 3.7
.012x + .42 = .1
EXAMPLES
Solve the equation.
.2x − 8 = 6
1.5 = .2x − .9
.04x + 1.2 = 80
EXAMPLES
Which equation is equivalent?
.3x − 7.2 = 8
.06x + .9 = 7
a)3x − 72 = 80
a)6x + 9 = 70
b)3x − 72 = 8
b)6x + 90 = 700
c)3x − 7.2 = 8
c)6x + 900 = 700
EXAMPLES
The county fair charges $.50 per ride and $10.25 to
get in. If you have $31.75, write and solve an
equation to find the number of rides (r) you can go
on.
EXAMPLES
Peter was a waiter that was paid at a rate of $7.50 per
hour plus tips. If he has earned $195 including $45 in
tips, write and solve an equation to determine how
many hours (h) he worked.
PRACTICE
Write an equivalent equation with whole numbers.
.009x − .8 = 8.2
PRACTICE
Solve the equations.
.5x + 8 = 14
.54 = .04x − .3
FINAL QUESTION
The county fair charges $1.50 per ride and $14.70 to
get in. If you have $29.70, write and solve an
equation to find the number of rides (r) you can go
on.