18
Holt Algebra 1 2-5 Solving for a Variable Warm Up Solve each equation. 1. 5 + x = –2 2. 8m = 43 3. 4. 0.3s + 0.6 = 1.5 5. 10k – 6 = 9k + 2 –7 3 19 8
Holt Algebra 1
2-5 Solving for a Variable
Warm UpSolve each equation.1. 5 + x = –22. 8m = 43 3.
4. 0.3s + 0.6 = 1.55. 10k – 6 = 9k + 2
–7
3
19
8
Holt Algebra 1
2-5 Solving for a Variable
Solve a formula for a given variable.Solve an equation in two or more variables for one of the variables.
Objectives
Holt Algebra 1
2-5 Solving for a Variable
formulaliteral equation
Vocabulary
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 VariableStep 1 Locate the variable you are asked to
solve for in the equation.Step 2 Identify the operations on this
variable and the order in which they are applied.
Step 3 Use inverse operations to undo operations and isolate the variable.
Holt Algebra 1
2-5 Solving for a Variable
Example 1
Locate t in the equation.
Solve the formula d = rt for t
Since t is multiplied by r, divide both sides by r to undo the multiplication.
d = rt
Holt Algebra 1
2-5 Solving for a Variable
Example 2The formula for the area of a triangle is A = bh, where b is the length of the base, and is the height. Solve for h.
Locate h in the equation. A = bhSince bh is multiplied by , divide both
sides by to undo the multiplication.2A = bh
Since h is multiplied by b, divide both sides by b to undo the multiplication.
Holt Algebra 1
2-5 Solving for a Variable
Dividing by a fraction is the same as multiplying by the reciprocal.
Remember!
Holt Algebra 1
2-5 Solving for a Variable
Example 3The formula for a person’s typing speed is ,where s is speed in words per minute, w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e.
Locate e in the equation.Since w–10e is divided by m,
multiply both sides by m to undo the division.
ms = w – 10e–w –w
ms – w = –10e
Since w is added to –10e, subtract w from both sides to undo the addition.
Holt Algebra 1
2-5 Solving for a Variable
Example 3 ContinuedThe formula for a person’s typing speed is ,where s is speed in words per minute, w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e.
Since e is multiplied by –10, divide both sides by –10 to undo the multiplication.
Holt Algebra 1
2-5 Solving for a Variable
Dividing by a fraction is the same as multiplying by the reciprocal.
Remember!
Holt Algebra 1
2-5 Solving for a Variable
Example 4The 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 Locate i in the equation.
Since gt is subtracted from i, add gt to both sides to undo the subtraction.
f = i – gt+ gt +gt
f + gt = i
Holt Algebra 1
2-5 Solving for a Variable
A formula is a type of literal equation. A literal equation is an equation with two or more variables. To solve for one of the variables, use inverse operations.
Holt Algebra 1
2-5 Solving for a Variable
Example 5
A. Solve x + y = 15 for x.x + y = 15 Locate x in the equation.
Since y is added to x, subtract y from both sides to undo the addition.
–y –yx = –y + 15
B. Solve pq = x for q. pq = x Locate q in the equation.
Since q is multiplied by p, divide both sides by p to undo the multiplication.
Holt Algebra 1
2-5 Solving for a Variable
Example 6
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
Example 7Solve for V
Locate V in the equation.
Since m is divided by V, multiply both sides by V to undo the division.VD = m
Since V is multiplied by D, divide both sides by D to undo the multiplication.
Holt Algebra 1
2-5 Solving for a Variable
Lesson Summary: Part 1Solve for the indicated variable.
1.
2.
3. 2x + 7y = 14 for y
4.
P = R – C for C C = R – P
for m m = x(k – 6 )
5. for C C = Rt + S
for h
Holt Algebra 1
2-5 Solving for a Variable
Lesson Summary: Part 2Euler’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.
6. Solve Euler’s formula for F.
7. How many faces does a polyhedron with 8 vertices and 12 edges have?
F = 2 – V + E
6
