Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{2})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 14x-\frac{35}{2}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{28}{ \color{blue}{2} }x- \frac{35}{ \color{blue}{2} })& = & (\frac{-18}{ \color{blue}{2} }x+ \frac{7}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 28x \color{red}{-35} & = & \color{red}{-18x} +7 \\\Leftrightarrow & 28x \color{red}{-35} \color{blue}{+35} \color{blue}{+18x} & = & \color{red}{-18x} +7 \color{blue}{+18x} \color{blue}{+35} \\\Leftrightarrow & 28x+18x& = & 7+35 \\\Leftrightarrow & \color{red}{46} x& = & 42 \\\Leftrightarrow & x = \frac{42}{46} & & \\\Leftrightarrow & x = \frac{21}{23} & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{7})& = & 2x+\frac{10}{7} \\\Leftrightarrow & -25x+\frac{25}{7}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x+ \frac{25}{ \color{blue}{7} })& = & (\frac{14}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+25} & = & \color{red}{14x} +10 \\\Leftrightarrow & -175x \color{red}{+25} \color{blue}{-25} \color{blue}{-14x} & = & \color{red}{14x} +10 \color{blue}{-14x} \color{blue}{-25} \\\Leftrightarrow & -175x-14x& = & 10-25 \\\Leftrightarrow & \color{red}{-189} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-189} & & \\\Leftrightarrow & x = \frac{5}{63} & & \\ & V = \left\{ \frac{5}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-48} & = & \color{red}{-50x} +15 \\\Leftrightarrow & 120x \color{red}{-48} \color{blue}{+48} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{+48} \\\Leftrightarrow & 120x+50x& = & 15+48 \\\Leftrightarrow & \color{red}{170} x& = & 63 \\\Leftrightarrow & x = \frac{63}{170} & & \\ & V = \left\{ \frac{63}{170} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{12}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+36} & = & \color{red}{147x} +28 \\\Leftrightarrow & 252x \color{red}{+36} \color{blue}{-36} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{-36} \\\Leftrightarrow & 252x-147x& = & 28-36 \\\Leftrightarrow & \color{red}{105} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{105} & & \\ & V = \left\{ \frac{-8}{105} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{50x} +45 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & -120x-50x& = & 45-24 \\\Leftrightarrow & \color{red}{-170} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-170} & & \\\Leftrightarrow & x = \frac{-21}{170} & & \\ & V = \left\{ \frac{-21}{170} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{10})& = & 2x+\frac{2}{5} \\\Leftrightarrow & 9x-\frac{9}{10}& = & 2x+\frac{2}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{-9} & = & \color{red}{20x} +4 \\\Leftrightarrow & 90x \color{red}{-9} \color{blue}{+9} \color{blue}{-20x} & = & \color{red}{20x} +4 \color{blue}{-20x} \color{blue}{+9} \\\Leftrightarrow & 90x-20x& = & 4+9 \\\Leftrightarrow & \color{red}{70} x& = & 13 \\\Leftrightarrow & x = \frac{13}{70} & & \\ & V = \left\{ \frac{13}{70} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+132} & = & \color{red}{275x} +25 \\\Leftrightarrow & -1320x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -1320x-275x& = & 25-132 \\\Leftrightarrow & \color{red}{-1595} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-1595} & & \\\Leftrightarrow & x = \frac{107}{1595} & & \\ & V = \left\{ \frac{107}{1595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{9})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{576}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{360}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 576x \color{red}{-64} & = & \color{red}{360x} +45 \\\Leftrightarrow & 576x \color{red}{-64} \color{blue}{+64} \color{blue}{-360x} & = & \color{red}{360x} +45 \color{blue}{-360x} \color{blue}{+64} \\\Leftrightarrow & 576x-360x& = & 45+64 \\\Leftrightarrow & \color{red}{216} x& = & 109 \\\Leftrightarrow & x = \frac{109}{216} & & \\ & V = \left\{ \frac{109}{216} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{3}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +15 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +15 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 15-132 \\\Leftrightarrow & \color{red}{-935} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{-935} & & \\\Leftrightarrow & x = \frac{117}{935} & & \\ & V = \left\{ \frac{117}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{-60} & = & \color{red}{490x} +63 \\\Leftrightarrow & 1050x \color{red}{-60} \color{blue}{+60} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+60} \\\Leftrightarrow & 1050x-490x& = & 63+60 \\\Leftrightarrow & \color{red}{560} x& = & 123 \\\Leftrightarrow & x = \frac{123}{560} & & \\ & V = \left\{ \frac{123}{560} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{5})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -30x-\frac{18}{5}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{126}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-126} & = & \color{red}{245x} +20 \\\Leftrightarrow & -1050x \color{red}{-126} \color{blue}{+126} \color{blue}{-245x} & = & \color{red}{245x} +20 \color{blue}{-245x} \color{blue}{+126} \\\Leftrightarrow & -1050x-245x& = & 20+126 \\\Leftrightarrow & \color{red}{-1295} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-1295} & & \\\Leftrightarrow & x = \frac{-146}{1295} & & \\ & V = \left\{ \frac{-146}{1295} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{3})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{16}{3}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x- \frac{48}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{-48} & = & \color{red}{-63x} +10 \\\Leftrightarrow & 108x \color{red}{-48} \color{blue}{+48} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{+48} \\\Leftrightarrow & 108x+63x& = & 10+48 \\\Leftrightarrow & \color{red}{171} x& = & 58 \\\Leftrightarrow & x = \frac{58}{171} & & \\ & V = \left\{ \frac{58}{171} \right\} & \\\end{align}\)