Pre-Algebra 10-5 Solving for a Variable 10-5 Solving for a Variable Pre-Algebra Warm Up Warm Up...
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Transcript of Pre-Algebra 10-5 Solving for a Variable 10-5 Solving for a Variable Pre-Algebra Warm Up Warm Up...
Pre-Algebra
10-5 Solving for a Variable10-5 Solving for a Variable
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
10-5 Solving for a Variable
Warm UpSolve.
1. 8x – 9 = 23
2. 9x + 12 = 4x + 37
3. 6x – 8 = 7x + 3
4. x + 3 =
x = 4
x = 5
x = –11
Pre-Algebra
10-5 Solving for a Variable
12
18
23 4x = – , or –5 3
4
Pre-Algebra
10-5 Solving for a Variable
Problem of the Day
The formula A = 4r2 gives the surface area of a geometric figure. Solve the formula for r.
Can you identify what the geometric figure is?sphere
Pre-Algebra
10-5 Solving for a Variable
Learn to solve an equation for a variable.
Pre-Algebra
10-5 Solving for a Variable
If an equation contains more than one variable, you can sometimes isolate one of the variables by using inverse operations. You can add and subtract any variable quantity on both sides of an equation.
Pre-Algebra
10-5 Solving for a Variable
Solve for the indicated variable.
Additional Example 1A: Solving for a Variable by Addition or Subtraction
A. Solve a – b + 1 = c for a.
a – b + 1 = c
+ b – 1 + b – 1 Add b and subtract 1 from both sides.
a = c + b – 1 Isolate a.
Pre-Algebra
10-5 Solving for a Variable
Solve for the indicated variable.
Additional Example 1B: Solving for a Variable by Addition or Subtraction
B. Solve a – b + 1 = c for b.
a – b + 1 = c– a – 1 – a – 1 Subtract a and 1 from both
sides.
–b = c – a – 1 Isolate b.
Multiply both sides by –1.–1 (–b) = –1 (c – a – 1)
b = –c + a + 1 Isolate b.
Pre-Algebra
10-5 Solving for a Variable
Solve for the indicated variable.
Try This: Example 1A
A. Solve y – b + 3 = c for y.
y – b + 3 = c
+ b – 3 + b – 3 Add b and subtract 3 from both sides.
y = c + b – 3 Isolate y.
Pre-Algebra
10-5 Solving for a Variable
Solve for the indicated variable.
Try This: Example 1B
B. Solve p – w + 4 = f for w.
p – w + 4 = f– p – 4 – p – 4 Subtract p and 4 from both
sides.
–w = f – p – 4 Isolate w.
Multiply both sides by –1.–1 (–w) = –1 (f – p – 4)
w = –f + p + 4 Isolate w.
Pre-Algebra
10-5 Solving for a Variable
To isolate a variable, you can multiply or divide both sides of an equation by a variable if it can never be equal to 0. You can also take the square root of both sides of an equation that cannot have negative values.
Pre-Algebra
10-5 Solving for a Variable
Solve for the indicated variable. Assume all values are positive.
Additional Example 2A: Solving for a Variable by Division or Square Roots
A. Solve A = s2 for s.
A = s2
√A = s Isolate s.
√A = √s2 Take the square root of both sides.
Pre-Algebra
10-5 Solving for a VariableAdditional Example 2B: Solving for a Variable by Division
or Square Roots
B. Solve V = IR for R.
V = IR
= Divide both sides by I.IRI
VI
IV= R Isolate R.
Solve for the indicated variable. Assume all values are positive.
Pre-Algebra
10-5 Solving for a VariableAdditional Example 2C: Solving for a Variable by Division
or Square Roots
C. Solve the formula for the area of a trapezoid for h. Assume all values are positive.
A = h(b1 + b2)12 Write the formula.
2 • A = 2 • h(b1 + b2)12 Multiply both sides by 2.
2A = h(b1 + b2)
2A(b1 + b2)
= h Isolate h.
2A(b1 + b2)
h(b1 + b2) (b1 + b2)
= Divide both sides by (b1 + b2).
Pre-Algebra
10-5 Solving for a Variable
Solve for the indicated variable. Assume all values are positive.
Try This: Example 2A
A. Solve w = g2 + 4 for g.
w = g2 + 4
√ w – 4 = g Isolate g.
√w – 4 = √g2
w – 4 = g2
– 4 – 4 Subtract 4 from both sides.
Take the square root of both sides.
Pre-Algebra
10-5 Solving for a Variable
B. Solve A = lw for w.
A = lw
= Divide both sides by l.lwl
Al
lA= w Isolate w.
Solve for the indicated variable. Assume all values are positive.
Try This: Example 2B
Pre-Algebra
10-5 Solving for a Variable
C. Solve s = 180(n – 2) for n.
s = 180(n – 2)
Solve for the indicated variable. Assume all values are positive.
Try This: Example 2C
s 180(n – 2)180 180
= Divide both sides by 180.
s180
= (n – 2)
Add 2 to both sides.
s180
+ 2 = n
+ 2 + 2
Pre-Algebra
10-5 Solving for a Variable
To find solutions (x, y), choose values for x substitute to find y.
Remember!
Pre-Algebra
10-5 Solving for a Variable
Additional Example 3: Solving for y and Graphing
Solve for y and graph 3x + 2y = 8.
3x + 2y = 8
–3x –3x
2y = –3x + 8
–3x + 82
2y2
=
y = + 4–3x2
x y
–2 7
0 4
2 1
4 –2
Pre-Algebra
10-5 Solving for a Variable
Additional Example 3 Continued
3x + 2y = 8
Pre-Algebra
10-5 Solving for a Variable
Try This: Example 3
Solve for y and graph 4x + 3y = 12.
4x + 3y = 12
–4x – 4x
3y = –4x + 12
–4x + 12 3
3y3
=
y = + 4–4x3
x y
–3 8
0 4
3 0
6 –4
Pre-Algebra
10-5 Solving for a Variable
Try This: Example 3 Continued
x
y
–4 –2 2 4 6
10
86
2
–2
–4
44x + 3y = 12
–6
Pre-Algebra
10-5 Solving for a Variable
Lesson Quiz: Part 1
Solve for the indicated variable.
1. P = R – C for C.
2. P = 2l+ 2w for l.
3. V = Ah for h.
4. R = for S.
C = R - P
C – Rt = S
13C – S
t
= h3VA
= lP – 2w2
Pre-Algebra
10-5 Solving for a Variable
Lesson Quiz: Part 2
5. Solve for y and graph 2x + 7y = 14.
y = – + 2 2x 7