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Notes
Practice Problems
Solve for the variable
\(\textbf{1)}\)
The answer is \(x=5 \)
\(\,\,\,\,\,\displaystyle \frac{2x}{6}=\frac{5}{3}\)
\(\,\,\,\,\,\left(2x\right)\left(3\right)=\left(5\right)\left(6\right)\)
\(\,\,\,\,\,6x=30\)
\(\,\,\,\,\,x=5\)
\(\textbf{2)}\)
The answer is \(x=7 \)
\(\,\,\,\,\,\displaystyle \frac{x+2}{12}=\frac{x-1}{8}\)
\(\,\,\,\,\,\left(x+2\right)\left(8\right)=\left(x-1\right)\left(12\right)\)
\(\,\,\,\,\,8\left(x+2\right)=12\left(x-1\right)\)
\(\,\,\,\,\,8x+16=12x-12\)
\(\,\,\,\,\,28=4x\)
\(\,\,\,\,\,x=7\)
\(\textbf{3)}\)
The answer is \(x=9 \)
\(\,\,\,\,\,\displaystyle \frac{6}{3}=\frac{x}{4.5}\)
\(\,\,\,\,\,\left(6\right)\left(4.5\right)=\left(x\right)\left(3\right)\)
\(\,\,\,\,\,27=3x\)
\(\,\,\,\,\,x=9\)
\(\textbf{4)}\)
The answer is \(x=2 \)
\(\,\,\,\,\,\displaystyle \frac{x}{3}=\frac{10}{18-3}\)
\(\,\,\,\,\,\displaystyle \frac{x}{3}=\frac{10}{15}\)
\(\,\,\,\,\,\left(x\right)\left(15\right)=\left(10\right)\left(3\right)\)
\(\,\,\,\,\,15x=30\)
\(\,\,\,\,\,x=2\)
\(\textbf{5)}\)
The answer is \(x=3 \)
\(\,\,\,\,\,\displaystyle \frac{1}{1.5}=\frac{x}{6-1.5}\)
\(\,\,\,\,\,\displaystyle \frac{1}{1.5}=\frac{x}{4.5}\)
\(\,\,\,\,\,\left(1\right)\left(4.5\right)=\left(x\right)\left(1.5\right)\)
\(\,\,\,\,\,4.5=1.5x\)
\(\,\,\,\,\,x=3\)
\(\textbf{6)}\)
The answer is \(x=12 \)
\(\,\,\,\,\,\displaystyle \frac{x}{15}=\frac{8}{10}\)
\(\,\,\,\,\,\left(x\right)\left(10\right)=\left(8\right)\left(15\right)\)
\(\,\,\,\,\,10x=120\)
\(\,\,\,\,\,x=12\)
\(\textbf{7)}\)
The answer is \(x=8 \)
\(\,\,\,\,\,\displaystyle \frac{8}{6}=\frac{12}{x+1}\)
\(\,\,\,\,\,\left(8\right)\left(x+1\right)=\left(12\right)\left(6\right)\)
\(\,\,\,\,\,8\left(x+1\right)=72\)
\(\,\,\,\,\,8x+8=72\)
\(\,\,\,\,\,8x=64\)
\(\,\,\,\,\,x=8\)
\(\textbf{8)}\)
The answer is \(w=36 \)
\(\,\,\,\,\,\displaystyle \frac{6}{8}=\frac{21}{w-8}\)
\(\,\,\,\,\,\left(6\right)\left(w-8\right)=\left(21\right)\left(8\right)\)
\(\,\,\,\,\,6\left(w-8\right)=168\)
\(\,\,\,\,\,6w-48=168\)
\(\,\,\,\,\,6w=216\)
\(\,\,\,\,\,w=36\)
\(\textbf{9)}\)
The answer is \(x=8 \)
\(\,\,\,\,\,\displaystyle \frac{x+4}{9}=\frac{8}{6}\)
\(\,\,\,\,\,\left(x+4\right)\left(6\right)=\left(8\right)\left(9\right)\)
\(\,\,\,\,\,6\left(x+4\right)=72\)
\(\,\,\,\,\,6x+24=72\)
\(\,\,\,\,\,6x=48\)
\(\,\,\,\,\,x=8\)
\(\textbf{10)}\)
The answer is \(z=6 \)
\(\,\,\,\,\,\displaystyle \frac{4}{3}=\frac{z+2}{z}\)
\(\,\,\,\,\,\left(4\right)\left(z\right)=\left(z+2\right)\left(3\right)\)
\(\,\,\,\,\,4z=3\left(z+2\right)\)
\(\,\,\,\,\,4z=3z+6\)
\(\,\,\,\,\,z=6\)
\(\textbf{11)}\)
The answer is \(y=15 \)
\(\,\,\,\,\,\displaystyle \frac{y+5}{y}=\frac{12}{9}\)
\(\,\,\,\,\,\left(y+5\right)\left(9\right)=\left(12\right)\left(y\right)\)
\(\,\,\,\,\,9\left(y+5\right)=12y\)
\(\,\,\,\,\,9y+45=12y\)
\(\,\,\,\,\,45=3y\)
\(\,\,\,\,\,y=15\)
\(\textbf{12)}\)
The answer is \( x=11 \)
\(\,\,\,\,\,\displaystyle \frac{8}{x}=\frac{40}{55}\)
\(\,\,\,\,\,\left(8\right)\left(55\right)=\left(40\right)\left(x\right)\)
\(\,\,\,\,\,440=40x\)
\(\,\,\,\,\,x=11\)
\(\textbf{13)}\)
The answer is \( y=10 \)
\(\,\,\,\,\,\displaystyle \frac{20}{16}=\frac{y}{8}\)
\(\,\,\,\,\,\left(20\right)\left(8\right)=\left(y\right)\left(16\right)\)
\(\,\,\,\,\,160=16y\)
\(\,\,\,\,\,y=10\)
\(\textbf{14)}\)
The answer is \( x=16 \)
\(\,\,\,\,\,\displaystyle \frac{15}{12}=\frac{20}{x}\)
\(\,\,\,\,\,\left(15\right)\left(x\right)=\left(20\right)\left(12\right)\)
\(\,\,\,\,\,15x=240\)
\(\,\,\,\,\,x=16\)
\(\textbf{15)}\)
The answer is \( x=108 \)
\(\,\,\,\,\,\displaystyle \frac{22}{27}=\frac{88}{x}\)
\(\,\,\,\,\,\left(22\right)\left(x\right)=\left(88\right)\left(27\right)\)
\(\,\,\,\,\,22x=2{,}376\)
\(\,\,\,\,\,x=108\)
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