Practice Makes Perfect
Solve Equations with Constants on Both Sides
In the following exercises, solve the following equations with constants on both sides.
Exercise \(\PageIndex{1}\)
\(9 x-3=60\)
Exercise \(\PageIndex{2}\)
\(12 x-8=64\)
- Answer
-
\(x=6\)
Exercise \(\PageIndex{3}\)
\(14 w+5=117\)
Exercise \(\PageIndex{4}\)
\(15 y+7=97\)
- Answer
-
\(y=6\)
Exercise \(\PageIndex{5}\)
\(2 a+8=-28\)
Exercise \(\PageIndex{6}\)
\(3 m+9=-15\)
- Answer
-
\(m=-8\)
Exercise \(\PageIndex{7}\)
\(-62=8 n-6\)
Exercise \(\PageIndex{8}\)
\(-77=9 b-5\)
- Answer
-
\(b=-8\)
Exercise \(\PageIndex{9}\)
\(35=-13 y+9\)
Exercise \(\PageIndex{10}\)
\(60=-21 x-24\)
- Answer
-
\(x=-4\)
Exercise \(\PageIndex{11}\)
\(-12 p-9=9\)
Exercise \(\PageIndex{12}\)
\(-14 q-2=16\)
- Answer
-
\(q=-\frac{9}{7}\)
Solve Equations with Variables on Both Sides
In the following exercises, solve the following equations with variables on both sides.
Exercise \(\PageIndex{13}\)
\(19 z=18 z-7\)
Exercise \(\PageIndex{14}\)
\(21 k=20 k-11\)
- Answer
-
\(k=-11\)
Exercise \(\PageIndex{15}\)
\(9 x+36=15 x\)
Exercise \(\PageIndex{16}\)
\(8 x+27=11 x\)
- Answer
-
\(x=9\)
Exercise \(\PageIndex{17}\)
\(c=-3 c-20\)
Exercise \(\PageIndex{18}\)
\(b=-4 b-15\)
- Answer
-
\(b=-3\)
Exercise \(\PageIndex{19}\)
\(9 q=44-2 q\)
Exercise \(\PageIndex{20}\)
\(5 z=39-8 z\)
- Answer
-
\(z=3\)
Exercise \(\PageIndex{21}\)
\(6 y+\frac{1}{2}=5 y\)
Exercise \(\PageIndex{22}\)
\(4 x+\frac{3}{4}=3 x\)
- Answer
-
\(x=-\frac{3}{4}\)
Exercise \(\PageIndex{23}\)
\(-18 a-8=-22 a\)
Exercise \(\PageIndex{24}\)
\(-11 r-8=-7 r\)
- Answer
-
\(r=-2\)
Solve Equations with Variables and Constants on Both Sides
In the following exercises, solve the following equations with variables and constants on both sides.
Exercise \(\PageIndex{25}\)
\(8 x-15=7 x+3\)
Exercise \(\PageIndex{26}\)
\(6 x-17=5 x+2\)
- Answer
-
\(x=19\)
Exercise \(\PageIndex{27}\)
\(26+13 d=14 d+11\)
Exercise \(\PageIndex{28}\)
\(21+18 f=19 f+14\)
- Answer
-
\(f=7\)
Exercise \(\PageIndex{29}\)
\(2 p-1=4 p-33\)
Exercise \(\PageIndex{30}\)
\(12 q-5=9 q-20\)
- Answer
-
\(q=-5\)
Exercise \(\PageIndex{31}\)
\(4 a+5=-a-40\)
Exercise \(\PageIndex{32}\)
\(8 c+7=-3 c-37\)
- Answer
-
\(c=-4\)
Exercise \(\PageIndex{33}\)
\(5 y-30=-5 y+30\)
Exercise \(\PageIndex{34}\)
\(7 x-17=-8 x+13\)
- Answer
-
\(x=2\)
Exercise \(\PageIndex{35}\)
\(7 s+12=5+4 s\)
Exercise \(\PageIndex{36}\)
\(9 p+14=6+4 p\)
- Answer
-
\(p=-\frac{8}{5}\)
Exercise \(\PageIndex{37}\)
\(2 z-6=23-z\)
Exercise \(\PageIndex{38}\)
\(3 y-4=12-y\)
- Answer
-
\(y=4\)
Exercise \(\PageIndex{39}\)
\(\frac{5}{3} c-3=\frac{2}{3} c-16\)
Exercise \(\PageIndex{40}\)
\(\frac{7}{4} m-7=\frac{3}{4} m-13\)
- Answer
-
\(m=-6\)
Exercise \(\PageIndex{41}\)
\(8-\frac{2}{5} q=\frac{3}{5} q+6\)
Exercise \(\PageIndex{42}\)
\(11-\frac{1}{5} a=\frac{4}{5} a+4\)
- Answer
-
\(a=7\)
Exercise \(\PageIndex{43}\)
\(\frac{4}{3} n+9=\frac{1}{3} n-9\)
Exercise \(\PageIndex{44}\)
\(\frac{5}{4} a+15=\frac{3}{4} a-5\)
- Answer
-
\(a=-40\)
Exercise \(\PageIndex{45}\)
\(\frac{1}{4} y+7=\frac{3}{4} y-3\)
Exercise \(\PageIndex{46}\)
\(\frac{3}{5} p+2=\frac{4}{5} p-1\)
- Answer
-
\(p=15\)
Exercise \(\PageIndex{47}\)
\(14 n+8.25=9 n+19.60\)
Exercise \(\PageIndex{48}\)
\(13 z+6.45=8 z+23.75\)
- Answer
-
\(z=3.46\)
Exercise \(\PageIndex{49}\)
\(2.4 w-100=0.8 w+28\)
Exercise \(\PageIndex{50}\)
\(2.7 w-80=1.2 w+10\)
- Answer
-
\(w=60\)
Exercise \(\PageIndex{51}\)
\(5.6 r+13.1=3.5 r+57.2\)
Exercise \(\PageIndex{52}\)
\(6.6 x-18.9=3.4 x+54.7\)
- Answer
-
\(x=23\)
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?