Download Solve for the indicated variable.

10-5
10-5Solving
Solvingfor
fora aVariable
Variable
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
10-5 Solving for a Variable
Warm Up
Solve.
1. 8x – 9 = 23
x=4
2. 9x + 12 = 4x + 37
x=5
3. 6x – 8 = 7x + 3 x = –11
4. 1x + 3 = 1 x = – 23, or –5 3
4
2
8
4
Pre-Algebra
10-5 Solving for a Variable
Problem of the Day
The formula A = 4r2 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
Additional Example 1A: Solving for a Variable by
Addition or Subtraction
Solve for the indicated variable.
A. Solve a – b + 1 = c for a.
a–b+1=c
+b–1
+b–1
a
Pre-Algebra
=c+b–1
Add b and subtract 1 from
both sides.
Isolate a.
10-5 Solving for a Variable
Additional Example 1B: Solving for a Variable by
Addition or Subtraction
Solve for the indicated variable.
B. Solve a – b + 1 = c for b.
a–b+1=c
Subtract a and 1 from both
–a
–1
–a –1
sides.
–b
=c–a–1
Isolate b.
–1  (–b) = –1  (c – a – 1) Multiply both sides by –1.
b = –c + a + 1
Pre-Algebra
Isolate b.
10-5 Solving for a Variable
Try This: Example 1A
Solve for the indicated variable.
A. Solve y – b + 3 = c for y.
y–b+3=c
+b–3
+b–3
y
Pre-Algebra
=c+b–3
Add b and subtract 3 from
both sides.
Isolate y.
10-5 Solving for a Variable
Try This: Example 1B
Solve for the indicated variable.
B. Solve p – w + 4 = f for w.
p–w+4=f
Subtract p and 4 from both
–p
–4
–p –4
sides.
–w
=f–p–4
Isolate w.
–1  (–w) = –1  (f – p – 4) Multiply both sides by –1.
w = –f + p + 4
Pre-Algebra
Isolate w.
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.
Pre-Algebra
10-5 Solving for a Variable
Additional Example 2A: Solving for a Variable by
Division or Square Roots
Solve for the indicated variable. Assume all
values are positive.
A. Solve V = IR for R.
V = IR
V = IR
I
I
Divide both sides by I.
V= R
I
Isolate R.
Pre-Algebra
10-5 Solving for a Variable
Additional Example 2B: Solving for a Variable by
Division or Square Roots
B. Solve the formula for the area of a trapezoid
for h. Assume all values are positive.
A= 1
Write the formula.
2 h(b1 + b2)
2 A = 2 1
2 h(b1 + b2) Multiply both sides by 2.
2A = h(b1 + b2)
2A
= h(b1 + b2)
(b1 + b2)
(b1 + b2)
2A
=h
(b1 + b2)
Pre-Algebra
Divide both sides by
(b1 + b2).
Isolate h.
10-5 Solving for a Variable
Try This: Example 2A
Solve for the indicated variable. Assume all
values are positive.
A. Solve A = lw for w.
A = lw
A = lw
l
l
Divide both sides by l.
A= w
l
Isolate w.
Pre-Algebra
10-5 Solving for a Variable
Try This: Example 2B
Solve for the indicated variable. Assume all
values are positive.
B. Solve s = 180(n – 2) for n.
s = 180(n – 2)
s = 180(n – 2)
180
180
s = (n – 2)
180
+2
s +2=n
180
Pre-Algebra
+2
Divide both sides by 180.
Add 2 to both sides.
10-5 Solving for a Variable
Remember!
To find solutions (x, y), choose values for x
substitute to find y.
Pre-Algebra
10-5 Solving for a Variable
Additional Example 3: Solving for y
Solve for y:
3x + 2y =
–3x
3x + 2y = 8.
8
–3x
2y = –3x + 8
2y= –3x + 8
2
2
y = –3x
2 +4
Pre-Algebra
10-5 Solving for a Variable
Try This: Example 3
Solve for y and graph 4x + 3y = 12.
4x + 3y =
–4x
12
– 4x
3y = –4x + 12
3y= –4x + 12
3
3
y = –4x
3 +4
Pre-Algebra
x
y
–3
8
0
3
6
4
0
–4
10-5 Solving for a Variable
Try This: Example 3 Continued
y
10
8
6
4x + 3y = 12
4
2
–4 –2
–2
–4
–6
Pre-Algebra
2
4 6
x
10-5 Solving for a Variable
Lesson Quiz: Part 1
Solve for the indicated variable.
1. P = R – C for C.
C=R-P
2. P = 2l+ 2w for l. P – 2w= l
2
3V = h
3. V = 1 Ah for h.
3
A
4. R = C – S for S. C – Rt = S
t
Pre-Algebra