Transcript solving for a variable

2-5 Solving for a Variable
Warm Up
Solve each equation for the variable.
1. 5 + x = –2 –7
2. 8m = 43
3.
19
3
4. 10k – 6 = 9k + 2 8
Holt Algebra 1
for for
a Variable
2-5
Solving
a Variable
2-5 Solving
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Holt Algebra 1
2-5 Solving for a Variable
Objectives
Solve a formula for a given variable.
Solve an equation in two or more variables
for one of the variables.
Holt Algebra 1
2-5 Solving for a Variable
A formula is an equation that states a rule for a
relationship among quantities.
In the formula d = rt, d is isolated. You can
"rearrange" a formula to isolate any variable by
using inverse operations. This is called solving for a
variable.
Holt Algebra 1
2-5 Solving for a Variable
Solving for a Variable
Step 1 Locate the variable you are asked to
solve for in the equation. Circle it!
Step 2 Identify the operations on this
variable and the order in which they
are applied. List them!
Step 3 Use inverse operations to undo
operations and isolate the variable.
Holt Algebra 1
2-5 Solving for a Variable
Check It Out! Example 1
You are familiar with the formula d= rt .
Solve the formula d = rt for t.
d = rt
Holt Algebra 1
Locate t in the equation.
Since t is multiplied by r, divide both
sides by r to undo the multiplication.
2-5 Solving for a Variable
Check It Out! Example 2
The formula for an object’s final velocity is
f = i – gt, where i is the object’s initial
velocity, g is acceleration due to gravity,
and t is time. Solve for i.
f = i – gt
f = i – gt
+ gt
+gt
f + gt = i
Holt Algebra 1
Locate i in the equation.
Since gt is subtracted from i,
add gt to both sides to undo
the subtraction.
2-5 Solving for a Variable
Check It Out! Example 3b
Solve
for V
Locate V in the equation.
VD = m
Since m is divided by V, multiply
both sides by V to undo the
division.
Since V is multiplied by D, divide
both sides by D to undo the
multiplication.
Holt Algebra 1
2-5 Solving for a Variable
Euler’s formula, V – E + F = 2, relates the
number of vertices V, the number of edges E,
and the number of faces F of a polyhedron.
Solve Euler’s formula for F.
Holt Algebra 1
F=2–V+E
2-5 Solving for a Variable
Example 3: Solving Literal Equations
A. Solve x + y = 15 for x.
x + y = 15
–y –y
x
= –y + 15
B. Solve pq = x for q.
pq = x
Holt Algebra 1
Locate x in the equation.
Since y is added to x, subtract y
from both sides to undo the
addition.
Locate q in the equation.
Since q is multiplied by p, divide
both sides by p to undo the
multiplication.
2-5 Solving for a Variable
Check It Out! Example 3a
Solve 5 – b = 2t for t.
5 – b = 2t
Locate t in the equation.
Since t is multiplied by 2, divide
both sides by 2 to undo the
multiplication.
Holt Algebra 1
2-5 Solving for a Variable
You Try…
Solve for the indicated variable.
1.
for h
2. P = R – C for C
C=R–P
3. 2x + 7y = 14 for y
4.
for m
5.
for C
Holt Algebra 1
m = x(k – 6 )
C = Rt + S