Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & 8x+\frac{7}{6} \\\Leftrightarrow & -15x+\frac{6}{7}& = & 8x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-630}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{336}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -630x \color{red}{+36} & = & \color{red}{336x} +49 \\\Leftrightarrow & -630x \color{red}{+36} \color{blue}{-36} \color{blue}{-336x} & = & \color{red}{336x} +49 \color{blue}{-336x} \color{blue}{-36} \\\Leftrightarrow & -630x-336x& = & 49-36 \\\Leftrightarrow & \color{red}{-966} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-966} & & \\\Leftrightarrow & x = \frac{-13}{966} & & \\ & V = \left\{ \frac{-13}{966} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{5})& = & -9x+\frac{5}{12} \\\Leftrightarrow & 28x-\frac{14}{5}& = & -9x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1680}{ \color{blue}{60} }x- \frac{168}{ \color{blue}{60} })& = & (\frac{-540}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1680x \color{red}{-168} & = & \color{red}{-540x} +25 \\\Leftrightarrow & 1680x \color{red}{-168} \color{blue}{+168} \color{blue}{+540x} & = & \color{red}{-540x} +25 \color{blue}{+540x} \color{blue}{+168} \\\Leftrightarrow & 1680x+540x& = & 25+168 \\\Leftrightarrow & \color{red}{2220} x& = & 193 \\\Leftrightarrow & x = \frac{193}{2220} & & \\ & V = \left\{ \frac{193}{2220} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{4})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-75} & = & \color{red}{140x} +16 \\\Leftrightarrow & -180x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +16 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & -180x-140x& = & 16+75 \\\Leftrightarrow & \color{red}{-320} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-320} & & \\\Leftrightarrow & x = \frac{-91}{320} & & \\ & V = \left\{ \frac{-91}{320} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{3})& = & -9x+\frac{7}{8} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-96}{ \color{blue}{24} }x- \frac{64}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -96x \color{red}{-64} & = & \color{red}{-216x} +21 \\\Leftrightarrow & -96x \color{red}{-64} \color{blue}{+64} \color{blue}{+216x} & = & \color{red}{-216x} +21 \color{blue}{+216x} \color{blue}{+64} \\\Leftrightarrow & -96x+216x& = & 21+64 \\\Leftrightarrow & \color{red}{120} x& = & 85 \\\Leftrightarrow & x = \frac{85}{120} & & \\\Leftrightarrow & x = \frac{17}{24} & & \\ & V = \left\{ \frac{17}{24} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -6x-\frac{8}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-40} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -330x \color{red}{-40} \color{blue}{+40} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+40} \\\Leftrightarrow & -330x+385x& = & 22+40 \\\Leftrightarrow & \color{red}{55} x& = & 62 \\\Leftrightarrow & x = \frac{62}{55} & & \\ & V = \left\{ \frac{62}{55} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & -2x+\frac{8}{9} \\\Leftrightarrow & 35x+\frac{21}{8}& = & -2x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2520}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{-144}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2520x \color{red}{+189} & = & \color{red}{-144x} +64 \\\Leftrightarrow & 2520x \color{red}{+189} \color{blue}{-189} \color{blue}{+144x} & = & \color{red}{-144x} +64 \color{blue}{+144x} \color{blue}{-189} \\\Leftrightarrow & 2520x+144x& = & 64-189 \\\Leftrightarrow & \color{red}{2664} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{2664} & & \\ & V = \left\{ \frac{-125}{2664} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{147x} +28 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+30} \\\Leftrightarrow & -210x-147x& = & 28+30 \\\Leftrightarrow & \color{red}{-357} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-357} & & \\\Leftrightarrow & x = \frac{-58}{357} & & \\ & V = \left\{ \frac{-58}{357} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -4x+\frac{4}{3}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{+4} & = & \color{red}{15x} +4 \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{-4} \\\Leftrightarrow & -12x-15x& = & 4-4 \\\Leftrightarrow & \color{red}{-27} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-27} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{7})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -8x-\frac{8}{7}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{40}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{315x} +28 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & -280x-315x& = & 28+40 \\\Leftrightarrow & \color{red}{-595} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-595} & & \\\Leftrightarrow & x = \frac{-4}{35} & & \\ & V = \left\{ \frac{-4}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{-225x} +50 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & -540x+225x& = & 50-108 \\\Leftrightarrow & \color{red}{-315} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-315} & & \\\Leftrightarrow & x = \frac{58}{315} & & \\ & V = \left\{ \frac{58}{315} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{5})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 30x-\frac{18}{5}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-36} & = & \color{red}{-70x} +35 \\\Leftrightarrow & 300x \color{red}{-36} \color{blue}{+36} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{+36} \\\Leftrightarrow & 300x+70x& = & 35+36 \\\Leftrightarrow & \color{red}{370} x& = & 71 \\\Leftrightarrow & x = \frac{71}{370} & & \\ & V = \left\{ \frac{71}{370} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{9})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 28x-\frac{28}{9}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1764}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1764x \color{red}{-196} & = & \color{red}{-315x} +72 \\\Leftrightarrow & 1764x \color{red}{-196} \color{blue}{+196} \color{blue}{+315x} & = & \color{red}{-315x} +72 \color{blue}{+315x} \color{blue}{+196} \\\Leftrightarrow & 1764x+315x& = & 72+196 \\\Leftrightarrow & \color{red}{2079} x& = & 268 \\\Leftrightarrow & x = \frac{268}{2079} & & \\ & V = \left\{ \frac{268}{2079} \right\} & \\\end{align}\)