Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -2x+\frac{5}{2} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -2x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{+21} & = & \color{red}{-16x} +20 \\\Leftrightarrow & -224x \color{red}{+21} \color{blue}{-21} \color{blue}{+16x} & = & \color{red}{-16x} +20 \color{blue}{+16x} \color{blue}{-21} \\\Leftrightarrow & -224x+16x& = & 20-21 \\\Leftrightarrow & \color{red}{-208} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-208} & & \\\Leftrightarrow & x = \frac{1}{208} & & \\ & V = \left\{ \frac{1}{208} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 6x+\frac{10}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+90} & = & \color{red}{315x} +70 \\\Leftrightarrow & 378x \color{red}{+90} \color{blue}{-90} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{-90} \\\Leftrightarrow & 378x-315x& = & 70-90 \\\Leftrightarrow & \color{red}{63} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{63} & & \\ & V = \left\{ \frac{-20}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{3})& = & 9x+\frac{8}{11} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+154} & = & \color{red}{297x} +24 \\\Leftrightarrow & 924x \color{red}{+154} \color{blue}{-154} \color{blue}{-297x} & = & \color{red}{297x} +24 \color{blue}{-297x} \color{blue}{-154} \\\Leftrightarrow & 924x-297x& = & 24-154 \\\Leftrightarrow & \color{red}{627} x& = & -130 \\\Leftrightarrow & x = \frac{-130}{627} & & \\ & V = \left\{ \frac{-130}{627} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+50} & = & \color{red}{-245x} +21 \\\Leftrightarrow & 350x \color{red}{+50} \color{blue}{-50} \color{blue}{+245x} & = & \color{red}{-245x} +21 \color{blue}{+245x} \color{blue}{-50} \\\Leftrightarrow & 350x+245x& = & 21-50 \\\Leftrightarrow & \color{red}{595} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{595} & & \\ & V = \left\{ \frac{-29}{595} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{7})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-220} & = & \color{red}{-231x} +28 \\\Leftrightarrow & -1540x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +28 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & -1540x+231x& = & 28+220 \\\Leftrightarrow & \color{red}{-1309} x& = & 248 \\\Leftrightarrow & x = \frac{248}{-1309} & & \\\Leftrightarrow & x = \frac{-248}{1309} & & \\ & V = \left\{ \frac{-248}{1309} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{55x} +2 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +2 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & -264x-55x& = & 2-18 \\\Leftrightarrow & \color{red}{-319} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-319} & & \\\Leftrightarrow & x = \frac{16}{319} & & \\ & V = \left\{ \frac{16}{319} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{7})& = & -2x+\frac{3}{10} \\\Leftrightarrow & 15x+\frac{15}{7}& = & -2x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x+ \frac{150}{ \color{blue}{70} })& = & (\frac{-140}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{+150} & = & \color{red}{-140x} +21 \\\Leftrightarrow & 1050x \color{red}{+150} \color{blue}{-150} \color{blue}{+140x} & = & \color{red}{-140x} +21 \color{blue}{+140x} \color{blue}{-150} \\\Leftrightarrow & 1050x+140x& = & 21-150 \\\Leftrightarrow & \color{red}{1190} x& = & -129 \\\Leftrightarrow & x = \frac{-129}{1190} & & \\ & V = \left\{ \frac{-129}{1190} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{20}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{20}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+20} & = & \color{red}{-99x} +6 \\\Leftrightarrow & 220x \color{red}{+20} \color{blue}{-20} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{-20} \\\Leftrightarrow & 220x+99x& = & 6-20 \\\Leftrightarrow & \color{red}{319} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{319} & & \\ & V = \left\{ \frac{-14}{319} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{9})& = & 3x+\frac{9}{7} \\\Leftrightarrow & 4x+\frac{4}{9}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+28} & = & \color{red}{189x} +81 \\\Leftrightarrow & 252x \color{red}{+28} \color{blue}{-28} \color{blue}{-189x} & = & \color{red}{189x} +81 \color{blue}{-189x} \color{blue}{-28} \\\Leftrightarrow & 252x-189x& = & 81-28 \\\Leftrightarrow & \color{red}{63} x& = & 53 \\\Leftrightarrow & x = \frac{53}{63} & & \\ & V = \left\{ \frac{53}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{3})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -28x+\frac{14}{3}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+28} & = & \color{red}{-30x} +15 \\\Leftrightarrow & -168x \color{red}{+28} \color{blue}{-28} \color{blue}{+30x} & = & \color{red}{-30x} +15 \color{blue}{+30x} \color{blue}{-28} \\\Leftrightarrow & -168x+30x& = & 15-28 \\\Leftrightarrow & \color{red}{-138} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-138} & & \\\Leftrightarrow & x = \frac{13}{138} & & \\ & V = \left\{ \frac{13}{138} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & -7x+\frac{5}{9} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{-441x} +35 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{+441x} & = & \color{red}{-441x} +35 \color{blue}{+441x} \color{blue}{-90} \\\Leftrightarrow & -630x+441x& = & 35-90 \\\Leftrightarrow & \color{red}{-189} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-189} & & \\\Leftrightarrow & x = \frac{55}{189} & & \\ & V = \left\{ \frac{55}{189} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{6})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{25}{6}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-25} & = & \color{red}{42x} +8 \\\Leftrightarrow & 120x \color{red}{-25} \color{blue}{+25} \color{blue}{-42x} & = & \color{red}{42x} +8 \color{blue}{-42x} \color{blue}{+25} \\\Leftrightarrow & 120x-42x& = & 8+25 \\\Leftrightarrow & \color{red}{78} x& = & 33 \\\Leftrightarrow & x = \frac{33}{78} & & \\\Leftrightarrow & x = \frac{11}{26} & & \\ & V = \left\{ \frac{11}{26} \right\} & \\\end{align}\)