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# Linear Equations - PowerPoint by KVFeBY1l

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```									Linear Equations
Sections 10.1 – 10.3
►Ican recognize linear
equations.

►Ican solve equations
of the form x + B = C.

►Ican solve equations
of the form Ax = C

►Ican solve equations
of the form Ax + B = C
Write an Equation for the Following
►Iadded \$30 to my bank account and my

►Ipaid \$50 for 10 bags of cherries. How
much did each bag cost?

► Parkingcosts a flat rate of \$3.00 plus \$2.00
per hour. I spent \$13.00. How long was I
parked?
These Are Linear Equations
►x   + 30 = 330

► 10x   = 50

► 2x   + 3 = 13

► Anyequation that can be written in the form Ax +
B = C, where A, B, C are real numbers.
NOT Linear equations
► x2   + 5x -3 = 0

► |x   - 3| = 7

► 1/x   = 12

► √x    = 25.
Linear or Nonlinear?
►5   = 2x

►3   –s=¼

►3   – t2 = ¼

► 50   = ¼ r2
Goal: Solve Linear Equations
► Wehave simplified expressions with one or
sometimes more than one variable.

► Today  we are going to learn how to solve
linear equations in one variable.
Try This Problem
►I deposited \$30 into my bank account and
my new balance was \$330. What did I start
with?

► How    did you figure this out?

► Try   to solve this equation: x + 3 = 7.

This means: what value of x makes the sentence true?
Simplifying Expressions
► When you simplify expressions, you only
have one side of a scale. The weight
cannot change.
2(x+3)                      2x+6
Solving Equations
► When  you solve equations, you have both
sides of the scale! You can change the
weight, but the scale must balance!
x+3=7       x+3-3=7-3             x=4
Inverse Operations
► To solve x + 3 = 7, you subtract 3 from both
sides.

► To   solve x - 3 = 7, what do you do?

► Addition   and subtraction are inverse operations.

► We always use inverse operations to solve
equations.
More Examples
►5   – k = 12        If -x = a, then x = -a

► 5m   + 4 = 6m    6m – 5m = m (like terms)

►½   x – 5 = -1/2 x + 2
Try Some
►x   – 17 = 25

► 12   –r=7

►t   – ½ = 3/4

Simplify First
► Solve 5t – 4t + 6 = 9
► Simplify first, then solve

5t – 4t = t             t+6=9

► Solve 4x + 6 + 2x – 3 = 9 + 5x – 4
► Solve: 3(2+5x) – (1+14x) = 6

Use the distributive property!
I paid \$50 for 10 bags of cherries, how
► If
much did each bag of cherries cost?

► How   did you figure this out?

► Solve:   5x = 60
Try Some More
► Solve   -25p = 50

► Solve   2m = 15

► Solve   -6x = 14.
Fractions I
► Inalgebra, instead of writing x ¥ 3, we
write x/3.

► This is consistent with the notion that
division is multiplication by the reciprocal.

► To solve x/3 = 10, how do we undo the
division?
Fractions II
► What    about the equation 2/3 x = 6?

► To   divide by 2/3, multiply by the reciprocal.

► Since (3/2) £ (2/3) = 1, we now have:
x = (3/2) £ 6.

► Work    this out, what do we get?    x=9
Let’s do Another Together
► Solve:  7/5 x = 9/4
► What is the reciprocal of 7/5? 5/7
► Multiply both sides by 5/7.
► What do we have on the left? Just x
The product of a number with its reciprocal is 1!
► Forthe right, what is 5/7 times 9/4? 45/28
► What is our solution? x = 45/28
Try These
► Solve   y/12 = 5

► Solve   1/3 z = 19

► Solve   6/7 t = 9/5
Simplify First
like before, sometimes you have to
► Just
simplify before solving!

► Solve:   5x + 6x = 9

► Solve   7x – 2x = -25
Let’s Put These
Together!

► Parkingcosts a flat rate of \$3.00 plus \$2.00
per hour. I spent \$13.00. How long was I
parked?

► How   did you solve this problem?
The Easiest Way To Do This
► The equation for this problem is:
2h + 3 = 13.
► The variable h stands for hours.

subtract the 3 from both sides:
► First:
2h = 10
► Second: divide both sides by 2:
h = 5.
Another example
► Solve    3x -5 = 7      The order is the opposite!

Add 5 to both sides            3x = 12

► Second:    multiplication and division
Divide both sides by 3               x=4
Try These:
► Solve:   5x – 6 = 17

► Solve:   -4x + 2 = 9
► You can solve linear
equations using
inverse operations.

► If you have to deal