Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(-2(-5x+\frac{4}{11})=7x+\frac{5}{4}\)
2. \(4(-3x+\frac{5}{3})=-5x+\frac{3}{7}\)
3. \(7(2x+\frac{4}{5})=5x+\frac{9}{7}\)
4. \(5(5x-\frac{4}{3})=7x+\frac{10}{11}\)
5. \(-4(4x+\frac{5}{7})=-7x+\frac{10}{11}\)
6. \(-3(4x+\frac{5}{4})=-5x+\frac{3}{7}\)
7. \(7(-4x-\frac{3}{2})=2x+\frac{7}{8}\)
8. \(-4(-5x-\frac{2}{3})=7x+\frac{10}{9}\)
9. \(-6(2x+\frac{5}{7})=-5x+\frac{10}{11}\)
10. \(3(2x-\frac{5}{4})=7x+\frac{4}{3}\)
11. \(-3(-5x-\frac{5}{8})=7x+\frac{10}{9}\)
12. \(6(-4x-\frac{4}{5})=5x+\frac{10}{3}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{11})& = & 7x+\frac{5}{4} \\\Leftrightarrow & 10x-\frac{8}{11}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{32}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-32} & = & \color{red}{308x} +55 \\\Leftrightarrow & 440x \color{red}{-32} \color{blue}{+32} \color{blue}{-308x} & = & \color{red}{308x} +55 \color{blue}{-308x} \color{blue}{+32} \\\Leftrightarrow & 440x-308x& = & 55+32 \\\Leftrightarrow & \color{red}{132} x& = & 87 \\\Leftrightarrow & x = \frac{87}{132} & & \\\Leftrightarrow & x = \frac{29}{44} & & \\ & V = \left\{ \frac{29}{44} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{3})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{20}{3}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+140} & = & \color{red}{-105x} +9 \\\Leftrightarrow & -252x \color{red}{+140} \color{blue}{-140} \color{blue}{+105x} & = & \color{red}{-105x} +9 \color{blue}{+105x} \color{blue}{-140} \\\Leftrightarrow & -252x+105x& = & 9-140 \\\Leftrightarrow & \color{red}{-147} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{-147} & & \\\Leftrightarrow & x = \frac{131}{147} & & \\ & V = \left\{ \frac{131}{147} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{5})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 14x+\frac{28}{5}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{490}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 490x \color{red}{+196} & = & \color{red}{175x} +45 \\\Leftrightarrow & 490x \color{red}{+196} \color{blue}{-196} \color{blue}{-175x} & = & \color{red}{175x} +45 \color{blue}{-175x} \color{blue}{-196} \\\Leftrightarrow & 490x-175x& = & 45-196 \\\Leftrightarrow & \color{red}{315} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{315} & & \\ & V = \left\{ \frac{-151}{315} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{3})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 25x-\frac{20}{3}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{-220} & = & \color{red}{231x} +30 \\\Leftrightarrow & 825x \color{red}{-220} \color{blue}{+220} \color{blue}{-231x} & = & \color{red}{231x} +30 \color{blue}{-231x} \color{blue}{+220} \\\Leftrightarrow & 825x-231x& = & 30+220 \\\Leftrightarrow & \color{red}{594} x& = & 250 \\\Leftrightarrow & x = \frac{250}{594} & & \\\Leftrightarrow & x = \frac{125}{297} & & \\ & V = \left\{ \frac{125}{297} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{7})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-220} & = & \color{red}{-539x} +70 \\\Leftrightarrow & -1232x \color{red}{-220} \color{blue}{+220} \color{blue}{+539x} & = & \color{red}{-539x} +70 \color{blue}{+539x} \color{blue}{+220} \\\Leftrightarrow & -1232x+539x& = & 70+220 \\\Leftrightarrow & \color{red}{-693} x& = & 290 \\\Leftrightarrow & x = \frac{290}{-693} & & \\\Leftrightarrow & x = \frac{-290}{693} & & \\ & V = \left\{ \frac{-290}{693} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x-\frac{15}{4}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-105} & = & \color{red}{-140x} +12 \\\Leftrightarrow & -336x \color{red}{-105} \color{blue}{+105} \color{blue}{+140x} & = & \color{red}{-140x} +12 \color{blue}{+140x} \color{blue}{+105} \\\Leftrightarrow & -336x+140x& = & 12+105 \\\Leftrightarrow & \color{red}{-196} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-196} & & \\\Leftrightarrow & x = \frac{-117}{196} & & \\ & V = \left\{ \frac{-117}{196} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{2})& = & 2x+\frac{7}{8} \\\Leftrightarrow & -28x-\frac{21}{2}& = & 2x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x- \frac{84}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{-84} & = & \color{red}{16x} +7 \\\Leftrightarrow & -224x \color{red}{-84} \color{blue}{+84} \color{blue}{-16x} & = & \color{red}{16x} +7 \color{blue}{-16x} \color{blue}{+84} \\\Leftrightarrow & -224x-16x& = & 7+84 \\\Leftrightarrow & \color{red}{-240} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-240} & & \\\Leftrightarrow & x = \frac{-91}{240} & & \\ & V = \left\{ \frac{-91}{240} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{3})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 20x+\frac{8}{3}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+24} & = & \color{red}{63x} +10 \\\Leftrightarrow & 180x \color{red}{+24} \color{blue}{-24} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{-24} \\\Leftrightarrow & 180x-63x& = & 10-24 \\\Leftrightarrow & \color{red}{117} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{117} & & \\ & V = \left\{ \frac{-14}{117} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-330} & = & \color{red}{-385x} +70 \\\Leftrightarrow & -924x \color{red}{-330} \color{blue}{+330} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{+330} \\\Leftrightarrow & -924x+385x& = & 70+330 \\\Leftrightarrow & \color{red}{-539} x& = & 400 \\\Leftrightarrow & x = \frac{400}{-539} & & \\\Leftrightarrow & x = \frac{-400}{539} & & \\ & V = \left\{ \frac{-400}{539} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{4})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 6x-\frac{15}{4}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{-45} & = & \color{red}{84x} +16 \\\Leftrightarrow & 72x \color{red}{-45} \color{blue}{+45} \color{blue}{-84x} & = & \color{red}{84x} +16 \color{blue}{-84x} \color{blue}{+45} \\\Leftrightarrow & 72x-84x& = & 16+45 \\\Leftrightarrow & \color{red}{-12} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-12} & & \\\Leftrightarrow & x = \frac{-61}{12} & & \\ & V = \left\{ \frac{-61}{12} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{15}{8}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1080}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1080x \color{red}{+135} & = & \color{red}{504x} +80 \\\Leftrightarrow & 1080x \color{red}{+135} \color{blue}{-135} \color{blue}{-504x} & = & \color{red}{504x} +80 \color{blue}{-504x} \color{blue}{-135} \\\Leftrightarrow & 1080x-504x& = & 80-135 \\\Leftrightarrow & \color{red}{576} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{576} & & \\ & V = \left\{ \frac{-55}{576} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -24x-\frac{24}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-72} & = & \color{red}{75x} +50 \\\Leftrightarrow & -360x \color{red}{-72} \color{blue}{+72} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+72} \\\Leftrightarrow & -360x-75x& = & 50+72 \\\Leftrightarrow & \color{red}{-435} x& = & 122 \\\Leftrightarrow & x = \frac{122}{-435} & & \\\Leftrightarrow & x = \frac{-122}{435} & & \\ & V = \left\{ \frac{-122}{435} \right\} & \\\end{align}\)