Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -16x+\frac{16}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{+80} & = & \color{red}{-245x} +28 \\\Leftrightarrow & -560x \color{red}{+80} \color{blue}{-80} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{-80} \\\Leftrightarrow & -560x+245x& = & 28-80 \\\Leftrightarrow & \color{red}{-315} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-315} & & \\\Leftrightarrow & x = \frac{52}{315} & & \\ & V = \left\{ \frac{52}{315} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{5})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+16} & = & \color{red}{90x} +25 \\\Leftrightarrow & -80x \color{red}{+16} \color{blue}{-16} \color{blue}{-90x} & = & \color{red}{90x} +25 \color{blue}{-90x} \color{blue}{-16} \\\Leftrightarrow & -80x-90x& = & 25-16 \\\Leftrightarrow & \color{red}{-170} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-170} & & \\\Leftrightarrow & x = \frac{-9}{170} & & \\ & V = \left\{ \frac{-9}{170} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & -4x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-45} & = & \color{red}{-48x} +32 \\\Leftrightarrow & -180x \color{red}{-45} \color{blue}{+45} \color{blue}{+48x} & = & \color{red}{-48x} +32 \color{blue}{+48x} \color{blue}{+45} \\\Leftrightarrow & -180x+48x& = & 32+45 \\\Leftrightarrow & \color{red}{-132} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-132} & & \\\Leftrightarrow & x = \frac{-7}{12} & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{25x} +3 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +3 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 60x-25x& = & 3-12 \\\Leftrightarrow & \color{red}{35} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{35} & & \\ & V = \left\{ \frac{-9}{35} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{4})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -9x+\frac{9}{4}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{+27} & = & \color{red}{-60x} +40 \\\Leftrightarrow & -108x \color{red}{+27} \color{blue}{-27} \color{blue}{+60x} & = & \color{red}{-60x} +40 \color{blue}{+60x} \color{blue}{-27} \\\Leftrightarrow & -108x+60x& = & 40-27 \\\Leftrightarrow & \color{red}{-48} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-48} & & \\\Leftrightarrow & x = \frac{-13}{48} & & \\ & V = \left\{ \frac{-13}{48} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & -5x+\frac{9}{8} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{+48} & = & \color{red}{-200x} +45 \\\Leftrightarrow & 240x \color{red}{+48} \color{blue}{-48} \color{blue}{+200x} & = & \color{red}{-200x} +45 \color{blue}{+200x} \color{blue}{-48} \\\Leftrightarrow & 240x+200x& = & 45-48 \\\Leftrightarrow & \color{red}{440} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{440} & & \\ & V = \left\{ \frac{-3}{440} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -9x+\frac{3}{11} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2464}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{24}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2464x \color{red}{+231} & = & \color{red}{-792x} +24 \\\Leftrightarrow & -2464x \color{red}{+231} \color{blue}{-231} \color{blue}{+792x} & = & \color{red}{-792x} +24 \color{blue}{+792x} \color{blue}{-231} \\\Leftrightarrow & -2464x+792x& = & 24-231 \\\Leftrightarrow & \color{red}{-1672} x& = & -207 \\\Leftrightarrow & x = \frac{-207}{-1672} & & \\\Leftrightarrow & x = \frac{207}{1672} & & \\ & V = \left\{ \frac{207}{1672} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{7})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -10x-\frac{20}{7}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-100} & = & \color{red}{245x} +56 \\\Leftrightarrow & -350x \color{red}{-100} \color{blue}{+100} \color{blue}{-245x} & = & \color{red}{245x} +56 \color{blue}{-245x} \color{blue}{+100} \\\Leftrightarrow & -350x-245x& = & 56+100 \\\Leftrightarrow & \color{red}{-595} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-595} & & \\\Leftrightarrow & x = \frac{-156}{595} & & \\ & V = \left\{ \frac{-156}{595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{7})& = & -2x+\frac{9}{10} \\\Leftrightarrow & 9x-\frac{6}{7}& = & -2x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{630}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-140}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 630x \color{red}{-60} & = & \color{red}{-140x} +63 \\\Leftrightarrow & 630x \color{red}{-60} \color{blue}{+60} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{+60} \\\Leftrightarrow & 630x+140x& = & 63+60 \\\Leftrightarrow & \color{red}{770} x& = & 123 \\\Leftrightarrow & x = \frac{123}{770} & & \\ & V = \left\{ \frac{123}{770} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{9})& = & 6x+\frac{3}{10} \\\Leftrightarrow & 35x-\frac{35}{9}& = & 6x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{3150}{ \color{blue}{90} }x- \frac{350}{ \color{blue}{90} })& = & (\frac{540}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 3150x \color{red}{-350} & = & \color{red}{540x} +27 \\\Leftrightarrow & 3150x \color{red}{-350} \color{blue}{+350} \color{blue}{-540x} & = & \color{red}{540x} +27 \color{blue}{-540x} \color{blue}{+350} \\\Leftrightarrow & 3150x-540x& = & 27+350 \\\Leftrightarrow & \color{red}{2610} x& = & 377 \\\Leftrightarrow & x = \frac{377}{2610} & & \\\Leftrightarrow & x = \frac{13}{90} & & \\ & V = \left\{ \frac{13}{90} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{11})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 6x-\frac{6}{11}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{-275x} +33 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{+275x} & = & \color{red}{-275x} +33 \color{blue}{+275x} \color{blue}{+30} \\\Leftrightarrow & 330x+275x& = & 33+30 \\\Leftrightarrow & \color{red}{605} x& = & 63 \\\Leftrightarrow & x = \frac{63}{605} & & \\ & V = \left\{ \frac{63}{605} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -8x+\frac{6}{5}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+42} & = & \color{red}{105x} +45 \\\Leftrightarrow & -280x \color{red}{+42} \color{blue}{-42} \color{blue}{-105x} & = & \color{red}{105x} +45 \color{blue}{-105x} \color{blue}{-42} \\\Leftrightarrow & -280x-105x& = & 45-42 \\\Leftrightarrow & \color{red}{-385} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-385} & & \\\Leftrightarrow & x = \frac{-3}{385} & & \\ & V = \left\{ \frac{-3}{385} \right\} & \\\end{align}\)