Practice Problems
\(\textbf{1)}\) \(3(x+2)=12\)
The answer is \(x=2\)
\(\,\,\,\,\,3(x+2)=12\)
\(\,\,\,\,\,3x+6=12\)
\(\,\,\,\,\,3x=6\)
\(\,\,\,\,\,x=2\)
\(\textbf{2)}\) \(5(2x-3)=15\)
The answer is \(x=3\)
\(\,\,\,\,\,5(2x-3)=15\)
\(\,\,\,\,\,10x-15=15\)
\(\,\,\,\,\,10x=30\)
\(\,\,\,\,\,x=3\)
\(\textbf{3)}\) \(4(2x+3)+x=39\)
The answer is \(x=3\)
\(\,\,\,\,\,\,4(2x+3)+x=39\)
\(\,\,\,\,\,\,8x+12+x=39\)
\(\,\,\,\,\,\,9x+12=39\)
\(\,\,\,\,\,\,9x=27\)
\(\,\,\,\,\,\,x=3\)
\(\,\,\,\,\,\,\)The answer is \(x=3\)
\(\textbf{4)}\) \(2x+4(x-1)=-4\)
The answer is \(x=0\)
\(\,\,\,\,\,2x+4(x-1)=-4\)
\(\,\,\,\,\,2x+4x-4=-4\)
\(\,\,\,\,\,6x-4=-4\)
\(\,\,\,\,\,6x=0\)
\(\,\,\,\,\,x=0\)
\(\textbf{5)}\) \(4(x+1)+2(3x+1)=16\)
The answer is \(x=1\)
\(\,\,\,\,\,4(x+1)+2(3x+1)=16\)
\(\,\,\,\,\,4x+4+6x+2=16\)
\(\,\,\,\,\,10x+6=16\)
\(\,\,\,\,\,10x=10\)
\(\,\,\,\,\,x=1\)
![Link to Youtube Video Solving Question Number 5](https://andymath.com/wp-content/uploads/2020/08/play-video.jpg")
\(\textbf{6)}\) \(4− (2− 3x) = 9\)
The answer is \(x = \frac{7}{3}\)
\(\,\,\,\,\,\,4+ -1(2− 3x) = 9 \,\,\,\) (Rewrite to clarify)
\(\,\,\,\,\,\,4 -2 + 3x = 9 \,\,\,\) (Distribute the -1)
\(\,\,\,\,\,\,2 + 3x = 9 \,\,\,\) (Simplify)
\(\,\,\,\,\,\,3x = 7 \,\,\,\) (Subtract 2 from both sides)
\(\,\,\,\,\,\,x = \frac{7}{3} \,\,\,\) (Divide both sides by 3)
\(\textbf{7)}\) \(3(2x+5)-4(x-1)=23\)
The answer is \(x=2\)
\(\textbf{8)}\) \(2(3x+5)-3(4x-3)=13\)
The answer is \(x=1\)
\(\,\,\,\,\,\,2(3x+5)-3(4x-3)=13\)
\(\,\,\,\,\,\,6x+10-12x+9=13\)
\(\,\,\,\,\,\,-6x+19=13\)
\(\,\,\,\,\,\,-6x=-6\)
\(\,\,\,\,\,\,\)The answer is \(x=1\)
\(\textbf{9)}\) \(3(4x-2)=18\)
The answer is \(x=2\)
\(\,\,\,\,\,3(4x-2)=18\)
\(\,\,\,\,\,12x-6=18\)
\(\,\,\,\,\,12x=24\)
\(\,\,\,\,\,x=2\)
\(\textbf{10)}\) \(5(x+3)-2(x-4)=27\)
The answer is \(x=\frac{4}{3}\)
\(\,\,\,\,\,5(x+3)-2(x-4)=27\)
\(\,\,\,\,\,5x+15-2x+8=27\)
\(\,\,\,\,\,3x+23=27\)
\(\,\,\,\,\,3x=4\)
\(\,\,\,\,\,x=\frac{4}{3}\)
\(\textbf{11)}\) \(6x+4(3x-1)=26\)
The answer is \(x=\frac{5}{3}\)
\(\,\,\,\,\,6x+4(3x-1)=26\)
\(\,\,\,\,\,6x+12x-4=26\)
\(\,\,\,\,\,18x=30\)
\(\,\,\,\,\,x=\frac{5}{3}\)
\(\textbf{12)}\) \(7(x-1)+2x=23\)
The answer is \(x=\frac{10}{3}\)
\(\,\,\,\,\,7(x-1)+2x=23\)
\(\,\,\,\,\,7x-7+2x=23\)
\(\,\,\,\,\,9x=30\)
\(\,\,\,\,\,x=\frac{10}{3}\)
\(\textbf{13)}\) \(2(x+4)-3(2x-1)=3\)
The answer is \(x=2\)
\(\,\,\,\,\,2(x+4)-3(2x-1)=3\)
\(\,\,\,\,\,2x+8-6x+3=3\)
\(\,\,\,\,\, -4x+11=3\)
\(\,\,\,\,\, -4x=-8\)
\(\,\,\,\,\,x=2\)
\(\textbf{14)}\) \(8x-2(x-5)=18\)
The answer is \(x=\frac{4}{3}\)
\(\,\,\,\,\,8x-2(x-5)=18\)
\(\,\,\,\,\,8x-2x+10=18\)
\(\,\,\,\,\,6x=8\)
\(\,\,\,\,\,x=\frac{4}{3}\)
\(\textbf{15)}\) \(9(x-2)+x=28\)
The answer is \(x=\frac{23}{5}\)
\(\,\,\,\,\,9(x-2)+x=28\)
\(\,\,\,\,\,9x-18+x=28\)
\(\,\,\,\,\,10x=46\)
\(\,\,\,\,\,x=\frac{23}{5}\)
\(\textbf{16)}\) \(6(x+3)-4x=18\)
The answer is \(x=0\)
\(\,\,\,\,\,6(x+3)-4x=18\)
\(\,\,\,\,\,6x+18-4x=18\)
\(\,\,\,\,\,2x=0\)
\(\,\,\,\,\,x=0\)
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