Practice Makes Perfect
Solve Equations with Fraction Coefficients
In the following exercises, solve each equation with fraction coefficients.
Exercise \(\PageIndex{1}\)
\(\frac{1}{4} x-\frac{1}{2}=-\frac{3}{4}\)
Exercise \(\PageIndex{2}\)
\(\frac{3}{4} x-\frac{1}{2}=\frac{1}{4}\)
- Answer
-
x=1
Exercise \(\PageIndex{3}\)
\(\frac{5}{6} y-\frac{2}{3}=-\frac{3}{2}\)
Exercise \(\PageIndex{4}\)
\(\frac{5}{6} y-\frac{1}{3}=-\frac{7}{6}\)
- Answer
-
\(y=-1\)
Exercise \(\PageIndex{5}\)
\(\frac{1}{2} a+\frac{3}{8}=\frac{3}{4}\)
Exercise \(\PageIndex{6}\)
\(\frac{5}{8} b+\frac{1}{2}=-\frac{3}{4}\)
- Answer
-
\(b=-2\)
Exercise \(\PageIndex{7}\)
\(2=\frac{1}{3} x-\frac{1}{2} x+\frac{2}{3} x\)
Exercise \(\PageIndex{8}\)
\(2=\frac{3}{5} x-\frac{1}{3} x+\frac{2}{5} x\)
- Answer
-
\(x=3\)
Exercise \(\PageIndex{9}\)
\(\frac{1}{4} m-\frac{4}{5} m+\frac{1}{2} m=-1\)
Exercise \(\PageIndex{10}\)
\(\frac{5}{6} n-\frac{1}{4} n-\frac{1}{2} n=-2\)
- Answer
-
\(n=-24\)
Exercise \(\PageIndex{11}\)
\(x+\frac{1}{2}=\frac{2}{3} x-\frac{1}{2}\)
Exercise \(\PageIndex{12}\)
\(x+\frac{3}{4}=\frac{1}{2} x-\frac{5}{4}\)
- Answer
-
\(x=-4\)
Exercise \(\PageIndex{13}\)
\(\frac{1}{3} w+\frac{5}{4}=w-\frac{1}{4}\)
Exercise \(\PageIndex{14}\)
\(\frac{3}{2} z+\frac{1}{3}=z-\frac{2}{3}\)
- Answer
-
\(z=-2\)
Exercise \(\PageIndex{15}\)
\(\frac{1}{2} x-\frac{1}{4}=\frac{1}{12} x+\frac{1}{6}\)
Exercise \(\PageIndex{16}\)
\(\frac{1}{2} a-\frac{1}{4}=\frac{1}{6} a+\frac{1}{12}\)
- Answer
-
\(a=1\)
Exercise \(\PageIndex{17}\)
\(\frac{1}{3} b+\frac{1}{5}=\frac{2}{5} b-\frac{3}{5}\)
Exercise \(\PageIndex{18}\)
\(\frac{1}{3} x+\frac{2}{5}=\frac{1}{5} x-\frac{2}{5}\)
- Answer
-
\(x=-6\)
Exercise \(\PageIndex{19}\)
\(1=\frac{1}{6}(12 x-6)\)
-
Exercise \(\PageIndex{20}\)
\(1=\frac{1}{5}(15 x-10)\)
- Answer
-
\(x=1\)
Exercise \(\PageIndex{21}\)
\(\frac{1}{4}(p-7)=\frac{1}{3}(p+5)\)
Exercise \(\PageIndex{22}\)
\(\frac{1}{5}(q+3)=\frac{1}{2}(q-3)\)
- Answer
-
\(q=7\)
Exercise \(\PageIndex{23}\)
\(\frac{1}{2}(x+4)=\frac{3}{4}\)
Exercise \(\PageIndex{24}\)
\(\frac{1}{3}(x+5)=\frac{5}{6}\)
- Answer
-
\(x=-\frac{5}{2}\)
Exercise \(\PageIndex{25}\)
\(\frac{5 q-8}{5}=\frac{2 q}{10}\)
Exercise \(\PageIndex{26}\)
\(\frac{4 m+2}{6}=\frac{m}{3}\)
- Answer
-
\(m=-1\)
Exercise \(\PageIndex{27}\)
\(\frac{4 n+8}{4}=\frac{n}{3}\)
Exercise \(\PageIndex{28}\)
\(\frac{3 p+6}{3}=\frac{p}{2}\)
- Answer
-
\(p=-4\)
Exercise \(\PageIndex{29}\)
\(\frac{u}{3}-4=\frac{u}{2}-3\)
Exercise \(\PageIndex{30}\)
\(\frac{v}{10}+1=\frac{v}{4}-2\)
- Answer
-
\(v=20\)
Exercise \(\PageIndex{31}\)
\(\frac{c}{15}+1=\frac{c}{10}-1\)
Exercise \(\PageIndex{32}\)
\(\frac{d}{6}+3=\frac{d}{8}+2\)
- Answer
-
\(d=-24\)
Exercise \(\PageIndex{33}\)
\(\frac{3 x+4}{2}+1=\frac{5 x+10}{8}\)
Exercise \(\PageIndex{34}\)
\(\frac{10 y-2}{3}+3=\frac{10 y+1}{9}\)
- Answer
-
\(y=-1\)
Exercise \(\PageIndex{35}\)
\(\frac{7 u-1}{4}-1=\frac{4 u+8}{5}\)
Exercise \(\PageIndex{36}\)
\(\frac{3 v-6}{2}+5=\frac{11 v-4}{5}\)
- Answer
-
\(v=4\)
Solve Equations with Decimal Coefficients
In the following exercises, solve each equation with decimal coefficients.
Exercise \(\PageIndex{37}\)
\(0.6 y+3=9\)
Exercise \(\PageIndex{38}\)
\(0.4 y-4=2\)
- Answer
-
\(y=15\)
Exercise \(\PageIndex{39}\)
\(3.6 j-2=5.2\)
Exercise \(\PageIndex{40}\)
\(2.1 k+3=7.2\)
- Answer
-
\(k=2\)
Exercise \(\PageIndex{41}\)
\(0.4 x+0.6=0.5 x-1.2\)
Exercise \(\PageIndex{42}\)
\(0.7 x+0.4=0.6 x+2.4\)
- Answer
-
\(x=20\)
Exercise \(\PageIndex{43}\)
\(0.23 x+1.47=0.37 x-1.05\)
Exercise \(\PageIndex{44}\)
\(0.48 x+1.56=0.58 x-0.64\)
- Answer
-
\(x=22\)
Exercise \(\PageIndex{45}\)
\(0.9 x-1.25=0.75 x+1.75\)
Exercise \(\PageIndex{46}\)
\(1.2 x-0.91=0.8 x+2.29\)
- Answer
-
\(x=8\)
Exercise \(\PageIndex{47}\)
\(0.05 n+0.10(n+8)=2.15\)
Exercise \(\PageIndex{48}\)
\(0.05 n+0.10(n+7)=3.55\)
- Answer
-
\(n=19\)
Exercise \(\PageIndex{49}\)
\(0.10 d+0.25(d+5)=4.05\)
Exercise \(\PageIndex{50}\)
\(0.10 d+0.25(d+7)=5.25\)
- Answer
-
\(d=10\)
Exercise \(\PageIndex{51}\)
\(0.05(q-5)+0.25 q=3.05\)
Exercise \(\PageIndex{52}\)
\(0.05(q-8)+0.25 q=4.10\)
- Answer
-
\(q=15\)
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?