Literal Equations Worksheet

Name: ____________________________
Date: ____________________________
Grade: ___________________________

What Are Literal Equations?

A literal equation contains more than one variable. The goal is to solve for one variable in terms of the other variables.

Example:
Solve for x: y=x+5

Subtract 5 from both sides: x=y−5

Part A – Solve for the Given Variable

Solve each equation for the variable shown.

y=x+7, solve for x.
x= __________________
y=x−9, solve for x.
x= __________________
y=4x, solve for x.
x= __________________
y=5x, solve for x.
x= __________________
a=b+c, solve for b.
b= __________________
m=n−p, solve for n.
n= __________________
P=2l+2w, solve for l.
l= __________________
A=lw, solve for w.
w= __________________
d=rt, solve for t.
t= __________________
V=lwh, solve for h.
h= __________________

Part B – One-Step Literal Equations

x+a=b, solve for x.
x−a=b, solve for x.
ax=b, solve for x.
ax=b, solve for x.
y+8=x, solve for y.
p−6=q, solve for p.
7m=n, solve for m.
4r=s, solve for r.
c+d=e, solve for c.
f−g=h, solve for f.

Part C – Two-Step Literal Equations

Solve for the indicated variable.

y=3x+5, solve for x.
x= __________________
y=4x−7, solve for x.
x= __________________
y=2x+6, solve for x.
x= __________________
y=3x−8, solve for x.
x= __________________
a=5b+c, solve for b.
b= __________________
m=2n−p, solve for n.
n= __________________
q=4r+s, solve for r.
r= __________________
A=3x+2y, solve for x.
x= __________________
C=2πr, solve for r.
r= __________________
F=59C+32, solve for C.
C= __________________

Part D – Geometry Formulas

Rearrange each formula to solve for the requested variable.

A=lw, solve for l.
A=lw, solve for w.
P=2l+2w, solve for w.
A=21bh, solve for h.
A=21bh, solve for b.
V=lwh, solve for l.
V=lwh, solve for w.
C=2πr, solve for r.
A=πr2, solve for r.
d=rt, solve for r.

Part E – Science and Everyday Formulas

F=ma, solve for m.
F=ma, solve for a.
v=td, solve for d.
v=td, solve for t.
I=tQ, solve for Q.
I=tQ, solve for t.
P=IV, solve for I.
P=IV, solve for V.
D=Vm, solve for m.
D=Vm, solve for V.

Part F – Multiple Choice

Solve y=x+12 for x.
A. x=y+12
B. x=y−12
C. x=12−y
D. x=12y
Solve A=lw for w.
A. w=A−l
B. w=Al
C. w=lA
D. w=Al
Solve d=rt for r.
A. r=dt
B. r=td
C. r=dt
D. r=d−t
Solve F=ma for a.
A. a=Fm
B. a=mF
C. a=Fm
D. a=F−m
Solve P=2l+2w for l.
A. l=2P−2w
B. l=P−2w
C. l=2P+2w
D. l=2P−2w
Solve y=5x−10 for x.
A. x=5y−10
B. x=5y+10
C. x=5y+10
D. x=5(y−10)
Solve A=21bh for b.
A. b=2hA
B. b=h2A
C. b=2Ah
D. b=2Ah
Solve V=lwh for h.
A. h=Vlw
B. h=lwV
C. h=Vlw
D. h=V−lw
Solve C=2πr for r.
A. r=2πC
B. r=2πC
C. r=C2π
D. r=C−2π
Solve y=3x−4 for x.
A. x=3y−4
B. x=3y+4
C. x=3y+4
D. x=3(y−4)

Part G – Challenge Questions

y=ax+b, solve for x.
A=2(b1+b2)h, solve for h.
P=2l+2w, solve for l.
y=cmx+b, solve for x.
ax+b=c, solve for x.
y=a(x+b), solve for x.
M=zx+y, solve for y.
Q=cab, solve for b.
S=2πrh+2πr2, solve for h.
E=mc2, solve for m.

Answer Key

Part A

x=y−7
x=y+9
x=4y
x=5y
b=a−c
n=m+p
l=2P−2w
w=lA
t=rd
h=lwV

Part B

x=b−a
x=a+b
x=ab
x=ab
y=x−8
p=q+6
m=7n
r=4s
c=e−d
f=h+g

Part C

x=3y−5
x=4y+7
x=2y−6
x=3y+8
b=5a−c
n=2m+p
r=4q−s
x=3A−2y
r=2πC
C=95(F−32)

Part D

l=wA
w=lA
w=2P−2l
h=b2A
b=h2A
l=whV
w=lhV
r=2πC
r=πA
r=td

Part E

m=aF
a=mF
d=vt
t=vd
Q=It
t=IQ
I=VP
V=IP
m=DV
V=Dm

Part F

Part G

x=ay−b
h=b1+b22A
l=2P−2w
x=mcy−b
x=ac−b
x=ay−b
y=Mz−x
b=aQc
h=2πrS−2πr2
m=c2E