Solve Linear Equations by Grouping - Process
Read this topicExplanations 3
- (Video) Solve Linear Equations by Grouping by PatrickJMT Patrick JMT has a good video example of a linear equation he solves by grouping. Summary\large{\text{Summary}}Summary He…
By Ben Ferrara, Zora Gilbert, Alex Federspiel, Amy Feraco, Jonathan Heller
- Solving a linear equation breaks down to a few key steps: Use the distributive property to get rid of parentheses. The reason we do this is so we can more easily combine like te…
By Vatsal Ojha, Alex Federspiel, Caroline K, Anusha Rahman
- Solve by Grouping Solving linear equations by grouping is pretty simple once you get the hang of it. All you have to do is use operations (addition, subtraction, multiplication,…
By Amy Feraco, Alex Federspiel, Anusha Rahman
Problems 27
- Does the equation x+6x+3=3x+3+2\frac{x+6}{x+3} = \frac{3}{x+3} + 2x+3x+6=x+33+2 have real solutions?
- Solve for xxx. 5x+7=13+8x5x+7=13+8x5x+7=13+8x
- Solve for xxx. −6x−4x+3=−8x−9−6x−4x+3=−8x−9−6x−4x+3=−8x−9
- Solve for xxx. −14+5x+8−x=2+5x−14+5x+8−x=2+5x−14+5x+8−x=2+5x
- Solve for xxx. −7x+4(1+4x)=−3x−14−7x+4(1+4x)=−3x−14−7x+4(1+4x)=−3x−14
- Solve for xxx. 4x−50=6(−2x+3)4x−50=6(−2x+3)4x−50=6(−2x+3)
- Solve for xxx. 10x+3(5x−3)=5(6x+4)−710x+3(5x−3)=5(6x+4)−710x+3(5x−3)=5(6x+4)−7
- Solve for xxx. −4(x−1)+9(x−3)=7x+7−6x−4(x−1)+9(x−3)=7x+7−6x−4(x−1)+9(x−3)=7x+7−6x
- Solve for xxx. 54 +23 x=32 x\frac{5}{4}\ +\frac{2}{3}\ x=\frac{3}{2}\ x45 +32 x=23 x
- Solve for xxx. 14(x+34)=x−16\frac{1}{4}\left(x+\frac{3}{4}\right)=\frac{x}{-16}41(x+43)=−16x
- Solve for xxx. −(1.49x+0.04)=1.01x3.23-(1.49x+0.04)=\frac{1.01x}{3.23}−(1.49x+0.04)=3.231.01x Round to the nearest hundredth.
- Solve for xxx in the following equation. 2.75x+34.25=42.5+1.75x2.75x+34.25=42.5+1.75x2.75x+34.25=42.5+1.75x
- Solve for xxx. 4(2x+5)=2(6x−8)4(2x+5)=2(6x-8)4(2x+5)=2(6x−8)
- Solve for xxx. 3(10−5x)=−3(14−7x)3(10-5x)=-3(14-7x)3(10−5x)=−3(14−7x)
- Solve for xxx. 9(8x+3)=−6(9x+6)9(8x+3)=-6(9x+6)9(8x+3)=−6(9x+6)
- Solve for xxx. 63x=36x+16^{3x}=36^{x+1}63x=36x+1
- Solve for xxx. 25−2x=56x−325^{-2x}=5^{6x-3}25−2x=56x−3
- Solve for xxx. 42x2x−3 =1\frac{4^{2x}}{2^{x-3}}\ =12x−342x =1
- Solve for xxx. 31−x3x =95x\frac{3^{1-x}}{3^{x}}\ =9^{5x}3x31−x =95x
- Solve for xxx. 32 x−34 x=23 x+103\frac{3}{2}\ x-\frac{3}{4}\ x=\frac{2}{3}\ x+\frac{10}{3}23 x−43 x=32 x+310
- Solve for xxx. 1828+12x=35(x+13)\frac{18}{28}+\frac{1}{2}x=\frac{3}{5}\left(x+\frac{1}{3}\right)2818+21x=53(x+31)
- Solve for xxx. 87 x−96 x=54 x−310\frac{8}{7}\ x-\frac{9}{6}\ x=\frac{5}{4}\ x-\frac{3}{10}78 x−69 x=45 x−103
- How many solutions does the following equation have? 12x+7=24x+9.\frac{1}{2x+7} = \frac{2}{4x+9}.2x+71=4x+92.
- Solve for xxx: 9(3)x−1=81x−2.\frac{9}{(\sqrt{3})^{x-1}} = 81^{x-2}.(3)x−19=81x−2. Write your answer as a fraction in simplest form, without spaces.
- Find the value of kkk for which the equation x−1x−3=x−kx−8\frac{x-1}{x-3} = \frac{x-k}{x-8}x−3x−1=x−8x−k has no solutions for xxx.
- If x+1+2x+2=4x+4x+1 + 2x+2= 4x+4x+1+2x+2=4x+4, then...
- If (x−2)+3(x−2)=2(x−2)(x-2)+3(x-2) = 2(x-2)(x−2)+3(x−2)=2(x−2), then...