Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{9})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -16x+\frac{20}{9}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-576}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -576x \color{red}{+80} & = & \color{red}{252x} +21 \\\Leftrightarrow & -576x \color{red}{+80} \color{blue}{-80} \color{blue}{-252x} & = & \color{red}{252x} +21 \color{blue}{-252x} \color{blue}{-80} \\\Leftrightarrow & -576x-252x& = & 21-80 \\\Leftrightarrow & \color{red}{-828} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-828} & & \\\Leftrightarrow & x = \frac{59}{828} & & \\ & V = \left\{ \frac{59}{828} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{2})& = & -8x+\frac{9}{2} \\\Leftrightarrow & 15x+\frac{25}{2}& = & -8x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{30}{ \color{blue}{2} }x+ \frac{25}{ \color{blue}{2} })& = & (\frac{-16}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 30x \color{red}{+25} & = & \color{red}{-16x} +9 \\\Leftrightarrow & 30x \color{red}{+25} \color{blue}{-25} \color{blue}{+16x} & = & \color{red}{-16x} +9 \color{blue}{+16x} \color{blue}{-25} \\\Leftrightarrow & 30x+16x& = & 9-25 \\\Leftrightarrow & \color{red}{46} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{46} & & \\\Leftrightarrow & x = \frac{-8}{23} & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{11})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 10x-\frac{6}{11}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-42} & = & \color{red}{231x} +66 \\\Leftrightarrow & 770x \color{red}{-42} \color{blue}{+42} \color{blue}{-231x} & = & \color{red}{231x} +66 \color{blue}{-231x} \color{blue}{+42} \\\Leftrightarrow & 770x-231x& = & 66+42 \\\Leftrightarrow & \color{red}{539} x& = & 108 \\\Leftrightarrow & x = \frac{108}{539} & & \\ & V = \left\{ \frac{108}{539} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{6}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+30} & = & \color{red}{-275x} +66 \\\Leftrightarrow & -660x \color{red}{+30} \color{blue}{-30} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-30} \\\Leftrightarrow & -660x+275x& = & 66-30 \\\Leftrightarrow & \color{red}{-385} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-385} & & \\\Leftrightarrow & x = \frac{-36}{385} & & \\ & V = \left\{ \frac{-36}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{3})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{8}{3}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{+8} & = & \color{red}{21x} +2 \\\Leftrightarrow & 18x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & 18x-21x& = & 2-8 \\\Leftrightarrow & \color{red}{-3} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-3} & & \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x- \frac{64}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{-64} & = & \color{red}{-140x} +21 \\\Leftrightarrow & 336x \color{red}{-64} \color{blue}{+64} \color{blue}{+140x} & = & \color{red}{-140x} +21 \color{blue}{+140x} \color{blue}{+64} \\\Leftrightarrow & 336x+140x& = & 21+64 \\\Leftrightarrow & \color{red}{476} x& = & 85 \\\Leftrightarrow & x = \frac{85}{476} & & \\\Leftrightarrow & x = \frac{5}{28} & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{8}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+24} & = & \color{red}{231x} +22 \\\Leftrightarrow & -198x \color{red}{+24} \color{blue}{-24} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-24} \\\Leftrightarrow & -198x-231x& = & 22-24 \\\Leftrightarrow & \color{red}{-429} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-429} & & \\\Leftrightarrow & x = \frac{2}{429} & & \\ & V = \left\{ \frac{2}{429} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -10x+\frac{8}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{+72} & = & \color{red}{315x} +40 \\\Leftrightarrow & -450x \color{red}{+72} \color{blue}{-72} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-72} \\\Leftrightarrow & -450x-315x& = & 40-72 \\\Leftrightarrow & \color{red}{-765} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-765} & & \\\Leftrightarrow & x = \frac{32}{765} & & \\ & V = \left\{ \frac{32}{765} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{9})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{-88} & = & \color{red}{-495x} +36 \\\Leftrightarrow & 594x \color{red}{-88} \color{blue}{+88} \color{blue}{+495x} & = & \color{red}{-495x} +36 \color{blue}{+495x} \color{blue}{+88} \\\Leftrightarrow & 594x+495x& = & 36+88 \\\Leftrightarrow & \color{red}{1089} x& = & 124 \\\Leftrightarrow & x = \frac{124}{1089} & & \\ & V = \left\{ \frac{124}{1089} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 12x+\frac{6}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+48} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 480x \color{red}{+48} \color{blue}{-48} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{-48} \\\Leftrightarrow & 480x+280x& = & 35-48 \\\Leftrightarrow & \color{red}{760} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{760} & & \\ & V = \left\{ \frac{-13}{760} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{5})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 4x-\frac{8}{5}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x- \frac{16}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{-16} & = & \color{red}{-30x} +9 \\\Leftrightarrow & 40x \color{red}{-16} \color{blue}{+16} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{+16} \\\Leftrightarrow & 40x+30x& = & 9+16 \\\Leftrightarrow & \color{red}{70} x& = & 25 \\\Leftrightarrow & x = \frac{25}{70} & & \\\Leftrightarrow & x = \frac{5}{14} & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 3x+\frac{5}{11} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-132} & = & \color{red}{165x} +25 \\\Leftrightarrow & 440x \color{red}{-132} \color{blue}{+132} \color{blue}{-165x} & = & \color{red}{165x} +25 \color{blue}{-165x} \color{blue}{+132} \\\Leftrightarrow & 440x-165x& = & 25+132 \\\Leftrightarrow & \color{red}{275} x& = & 157 \\\Leftrightarrow & x = \frac{157}{275} & & \\ & V = \left\{ \frac{157}{275} \right\} & \\\end{align}\)