Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +10 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 10+36 \\\Leftrightarrow & \color{red}{-255} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-255} & & \\\Leftrightarrow & x = \frac{-46}{255} & & \\ & V = \left\{ \frac{-46}{255} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{11})& = & -8x+\frac{7}{5} \\\Leftrightarrow & -25x-\frac{25}{11}& = & -8x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1375}{ \color{blue}{55} }x- \frac{125}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1375x \color{red}{-125} & = & \color{red}{-440x} +77 \\\Leftrightarrow & -1375x \color{red}{-125} \color{blue}{+125} \color{blue}{+440x} & = & \color{red}{-440x} +77 \color{blue}{+440x} \color{blue}{+125} \\\Leftrightarrow & -1375x+440x& = & 77+125 \\\Leftrightarrow & \color{red}{-935} x& = & 202 \\\Leftrightarrow & x = \frac{202}{-935} & & \\\Leftrightarrow & x = \frac{-202}{935} & & \\ & V = \left\{ \frac{-202}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -24x+\frac{12}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-528}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -528x \color{red}{+24} & = & \color{red}{110x} +99 \\\Leftrightarrow & -528x \color{red}{+24} \color{blue}{-24} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{-24} \\\Leftrightarrow & -528x-110x& = & 99-24 \\\Leftrightarrow & \color{red}{-638} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-638} & & \\\Leftrightarrow & x = \frac{-75}{638} & & \\ & V = \left\{ \frac{-75}{638} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 12x+\frac{6}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+42} & = & \color{red}{175x} +10 \\\Leftrightarrow & 420x \color{red}{+42} \color{blue}{-42} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{-42} \\\Leftrightarrow & 420x-175x& = & 10-42 \\\Leftrightarrow & \color{red}{245} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{245} & & \\ & V = \left\{ \frac{-32}{245} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{+154} & = & \color{red}{99x} +12 \\\Leftrightarrow & -462x \color{red}{+154} \color{blue}{-154} \color{blue}{-99x} & = & \color{red}{99x} +12 \color{blue}{-99x} \color{blue}{-154} \\\Leftrightarrow & -462x-99x& = & 12-154 \\\Leftrightarrow & \color{red}{-561} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{-561} & & \\\Leftrightarrow & x = \frac{142}{561} & & \\ & V = \left\{ \frac{142}{561} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{6})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{25}{6}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1320}{ \color{blue}{66} }x- \frac{275}{ \color{blue}{66} })& = & (\frac{594}{ \color{blue}{66} }x+ \frac{36}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1320x \color{red}{-275} & = & \color{red}{594x} +36 \\\Leftrightarrow & 1320x \color{red}{-275} \color{blue}{+275} \color{blue}{-594x} & = & \color{red}{594x} +36 \color{blue}{-594x} \color{blue}{+275} \\\Leftrightarrow & 1320x-594x& = & 36+275 \\\Leftrightarrow & \color{red}{726} x& = & 311 \\\Leftrightarrow & x = \frac{311}{726} & & \\ & V = \left\{ \frac{311}{726} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{11})& = & -4x+\frac{5}{11} \\\Leftrightarrow & -15x-\frac{25}{11}& = & -4x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x- \frac{25}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{-25} & = & \color{red}{-44x} +5 \\\Leftrightarrow & -165x \color{red}{-25} \color{blue}{+25} \color{blue}{+44x} & = & \color{red}{-44x} +5 \color{blue}{+44x} \color{blue}{+25} \\\Leftrightarrow & -165x+44x& = & 5+25 \\\Leftrightarrow & \color{red}{-121} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-121} & & \\\Leftrightarrow & x = \frac{-30}{121} & & \\ & V = \left\{ \frac{-30}{121} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{3})& = & 3x+\frac{9}{8} \\\Leftrightarrow & 8x+\frac{20}{3}& = & 3x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{192}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 192x \color{red}{+160} & = & \color{red}{72x} +27 \\\Leftrightarrow & 192x \color{red}{+160} \color{blue}{-160} \color{blue}{-72x} & = & \color{red}{72x} +27 \color{blue}{-72x} \color{blue}{-160} \\\Leftrightarrow & 192x-72x& = & 27-160 \\\Leftrightarrow & \color{red}{120} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{120} & & \\ & V = \left\{ \frac{-133}{120} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+2)& = & 8x+\frac{4}{11} \\\Leftrightarrow & -21x-14& = & 8x+\frac{4}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x- \frac{154}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{-154} & = & \color{red}{88x} +4 \\\Leftrightarrow & -231x \color{red}{-154} \color{blue}{+154} \color{blue}{-88x} & = & \color{red}{88x} +4 \color{blue}{-88x} \color{blue}{+154} \\\Leftrightarrow & -231x-88x& = & 4+154 \\\Leftrightarrow & \color{red}{-319} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-319} & & \\\Leftrightarrow & x = \frac{-158}{319} & & \\ & V = \left\{ \frac{-158}{319} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{5})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -9x-\frac{6}{5}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-42} & = & \color{red}{175x} +30 \\\Leftrightarrow & -315x \color{red}{-42} \color{blue}{+42} \color{blue}{-175x} & = & \color{red}{175x} +30 \color{blue}{-175x} \color{blue}{+42} \\\Leftrightarrow & -315x-175x& = & 30+42 \\\Leftrightarrow & \color{red}{-490} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-490} & & \\\Leftrightarrow & x = \frac{-36}{245} & & \\ & V = \left\{ \frac{-36}{245} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{5})& = & -3x+\frac{8}{7} \\\Leftrightarrow & 20x+\frac{8}{5}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+56} & = & \color{red}{-105x} +40 \\\Leftrightarrow & 700x \color{red}{+56} \color{blue}{-56} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{-56} \\\Leftrightarrow & 700x+105x& = & 40-56 \\\Leftrightarrow & \color{red}{805} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{805} & & \\ & V = \left\{ \frac{-16}{805} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{9})& = & 8x+\frac{7}{10} \\\Leftrightarrow & -15x-\frac{10}{9}& = & 8x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1350}{ \color{blue}{90} }x- \frac{100}{ \color{blue}{90} })& = & (\frac{720}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1350x \color{red}{-100} & = & \color{red}{720x} +63 \\\Leftrightarrow & -1350x \color{red}{-100} \color{blue}{+100} \color{blue}{-720x} & = & \color{red}{720x} +63 \color{blue}{-720x} \color{blue}{+100} \\\Leftrightarrow & -1350x-720x& = & 63+100 \\\Leftrightarrow & \color{red}{-2070} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-2070} & & \\\Leftrightarrow & x = \frac{-163}{2070} & & \\ & V = \left\{ \frac{-163}{2070} \right\} & \\\end{align}\)