Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{5})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{-96} & = & \color{red}{200x} +35 \\\Leftrightarrow & -480x \color{red}{-96} \color{blue}{+96} \color{blue}{-200x} & = & \color{red}{200x} +35 \color{blue}{-200x} \color{blue}{+96} \\\Leftrightarrow & -480x-200x& = & 35+96 \\\Leftrightarrow & \color{red}{-680} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-680} & & \\\Leftrightarrow & x = \frac{-131}{680} & & \\ & V = \left\{ \frac{-131}{680} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{4})& = & 4x+\frac{4}{11} \\\Leftrightarrow & -15x+\frac{25}{4}& = & 4x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{275}{ \color{blue}{44} })& = & (\frac{176}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+275} & = & \color{red}{176x} +16 \\\Leftrightarrow & -660x \color{red}{+275} \color{blue}{-275} \color{blue}{-176x} & = & \color{red}{176x} +16 \color{blue}{-176x} \color{blue}{-275} \\\Leftrightarrow & -660x-176x& = & 16-275 \\\Leftrightarrow & \color{red}{-836} x& = & -259 \\\Leftrightarrow & x = \frac{-259}{-836} & & \\\Leftrightarrow & x = \frac{259}{836} & & \\ & V = \left\{ \frac{259}{836} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 24x+\frac{30}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+210} & = & \color{red}{-539x} +110 \\\Leftrightarrow & 1848x \color{red}{+210} \color{blue}{-210} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-210} \\\Leftrightarrow & 1848x+539x& = & 110-210 \\\Leftrightarrow & \color{red}{2387} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{2387} & & \\ & V = \left\{ \frac{-100}{2387} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{18}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{54}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+54} & = & \color{red}{-105x} +28 \\\Leftrightarrow & 252x \color{red}{+54} \color{blue}{-54} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{-54} \\\Leftrightarrow & 252x+105x& = & 28-54 \\\Leftrightarrow & \color{red}{357} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{357} & & \\ & V = \left\{ \frac{-26}{357} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & -8x+\frac{10}{9} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -8x+\frac{10}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-540}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-288}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -540x \color{red}{-135} & = & \color{red}{-288x} +40 \\\Leftrightarrow & -540x \color{red}{-135} \color{blue}{+135} \color{blue}{+288x} & = & \color{red}{-288x} +40 \color{blue}{+288x} \color{blue}{+135} \\\Leftrightarrow & -540x+288x& = & 40+135 \\\Leftrightarrow & \color{red}{-252} x& = & 175 \\\Leftrightarrow & x = \frac{175}{-252} & & \\\Leftrightarrow & x = \frac{-25}{36} & & \\ & V = \left\{ \frac{-25}{36} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{11})& = & 7x+\frac{7}{10} \\\Leftrightarrow & 25x-\frac{20}{11}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2750}{ \color{blue}{110} }x- \frac{200}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2750x \color{red}{-200} & = & \color{red}{770x} +77 \\\Leftrightarrow & 2750x \color{red}{-200} \color{blue}{+200} \color{blue}{-770x} & = & \color{red}{770x} +77 \color{blue}{-770x} \color{blue}{+200} \\\Leftrightarrow & 2750x-770x& = & 77+200 \\\Leftrightarrow & \color{red}{1980} x& = & 277 \\\Leftrightarrow & x = \frac{277}{1980} & & \\ & V = \left\{ \frac{277}{1980} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{9})& = & 9x+\frac{4}{9} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+8} & = & \color{red}{81x} +4 \\\Leftrightarrow & -72x \color{red}{+8} \color{blue}{-8} \color{blue}{-81x} & = & \color{red}{81x} +4 \color{blue}{-81x} \color{blue}{-8} \\\Leftrightarrow & -72x-81x& = & 4-8 \\\Leftrightarrow & \color{red}{-153} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-153} & & \\\Leftrightarrow & x = \frac{4}{153} & & \\ & V = \left\{ \frac{4}{153} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{3})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 10x+\frac{4}{3}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+4} & = & \color{red}{-21x} +8 \\\Leftrightarrow & 30x \color{red}{+4} \color{blue}{-4} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{-4} \\\Leftrightarrow & 30x+21x& = & 8-4 \\\Leftrightarrow & \color{red}{51} x& = & 4 \\\Leftrightarrow & x = \frac{4}{51} & & \\ & V = \left\{ \frac{4}{51} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{2})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -10x+\frac{15}{2}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{14}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{+165} & = & \color{red}{-154x} +14 \\\Leftrightarrow & -220x \color{red}{+165} \color{blue}{-165} \color{blue}{+154x} & = & \color{red}{-154x} +14 \color{blue}{+154x} \color{blue}{-165} \\\Leftrightarrow & -220x+154x& = & 14-165 \\\Leftrightarrow & \color{red}{-66} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{-66} & & \\\Leftrightarrow & x = \frac{151}{66} & & \\ & V = \left\{ \frac{151}{66} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -6x+\frac{8}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+88} & = & \color{red}{-231x} +18 \\\Leftrightarrow & -198x \color{red}{+88} \color{blue}{-88} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{-88} \\\Leftrightarrow & -198x+231x& = & 18-88 \\\Leftrightarrow & \color{red}{33} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{33} & & \\ & V = \left\{ \frac{-70}{33} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+36} & = & \color{red}{75x} +10 \\\Leftrightarrow & -360x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -360x-75x& = & 10-36 \\\Leftrightarrow & \color{red}{-435} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-435} & & \\\Leftrightarrow & x = \frac{26}{435} & & \\ & V = \left\{ \frac{26}{435} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{9})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -25x-\frac{20}{9}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{-140} & = & \color{red}{567x} +18 \\\Leftrightarrow & -1575x \color{red}{-140} \color{blue}{+140} \color{blue}{-567x} & = & \color{red}{567x} +18 \color{blue}{-567x} \color{blue}{+140} \\\Leftrightarrow & -1575x-567x& = & 18+140 \\\Leftrightarrow & \color{red}{-2142} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-2142} & & \\\Leftrightarrow & x = \frac{-79}{1071} & & \\ & V = \left\{ \frac{-79}{1071} \right\} & \\\end{align}\)