Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{7})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -25x+\frac{20}{7}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-700}{ \color{blue}{28} }x+ \frac{80}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -700x \color{red}{+80} & = & \color{red}{252x} +21 \\\Leftrightarrow & -700x \color{red}{+80} \color{blue}{-80} \color{blue}{-252x} & = & \color{red}{252x} +21 \color{blue}{-252x} \color{blue}{-80} \\\Leftrightarrow & -700x-252x& = & 21-80 \\\Leftrightarrow & \color{red}{-952} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-952} & & \\\Leftrightarrow & x = \frac{59}{952} & & \\ & V = \left\{ \frac{59}{952} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -20x+\frac{15}{8}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-480}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -480x \color{red}{+45} & = & \color{red}{-168x} +80 \\\Leftrightarrow & -480x \color{red}{+45} \color{blue}{-45} \color{blue}{+168x} & = & \color{red}{-168x} +80 \color{blue}{+168x} \color{blue}{-45} \\\Leftrightarrow & -480x+168x& = & 80-45 \\\Leftrightarrow & \color{red}{-312} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-312} & & \\\Leftrightarrow & x = \frac{-35}{312} & & \\ & V = \left\{ \frac{-35}{312} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{7})& = & 8x+\frac{7}{3} \\\Leftrightarrow & 15x-\frac{15}{7}& = & 8x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-45} & = & \color{red}{168x} +49 \\\Leftrightarrow & 315x \color{red}{-45} \color{blue}{+45} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{+45} \\\Leftrightarrow & 315x-168x& = & 49+45 \\\Leftrightarrow & \color{red}{147} x& = & 94 \\\Leftrightarrow & x = \frac{94}{147} & & \\ & V = \left\{ \frac{94}{147} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{5})& = & -5x+\frac{9}{5} \\\Leftrightarrow & -28x+\frac{14}{5}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-140}{ \color{blue}{5} }x+ \frac{14}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -140x \color{red}{+14} & = & \color{red}{-25x} +9 \\\Leftrightarrow & -140x \color{red}{+14} \color{blue}{-14} \color{blue}{+25x} & = & \color{red}{-25x} +9 \color{blue}{+25x} \color{blue}{-14} \\\Leftrightarrow & -140x+25x& = & 9-14 \\\Leftrightarrow & \color{red}{-115} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-115} & & \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 9x+\frac{5}{12} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 9x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1200}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{540}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1200x \color{red}{+144} & = & \color{red}{540x} +25 \\\Leftrightarrow & 1200x \color{red}{+144} \color{blue}{-144} \color{blue}{-540x} & = & \color{red}{540x} +25 \color{blue}{-540x} \color{blue}{-144} \\\Leftrightarrow & 1200x-540x& = & 25-144 \\\Leftrightarrow & \color{red}{660} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{660} & & \\ & V = \left\{ \frac{-119}{660} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{11})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x-\frac{12}{11}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-108} & = & \color{red}{-495x} +22 \\\Leftrightarrow & -1188x \color{red}{-108} \color{blue}{+108} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{+108} \\\Leftrightarrow & -1188x+495x& = & 22+108 \\\Leftrightarrow & \color{red}{-693} x& = & 130 \\\Leftrightarrow & x = \frac{130}{-693} & & \\\Leftrightarrow & x = \frac{-130}{693} & & \\ & V = \left\{ \frac{-130}{693} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{3})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -35x-\frac{35}{3}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{175}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-175} & = & \color{red}{-45x} +18 \\\Leftrightarrow & -525x \color{red}{-175} \color{blue}{+175} \color{blue}{+45x} & = & \color{red}{-45x} +18 \color{blue}{+45x} \color{blue}{+175} \\\Leftrightarrow & -525x+45x& = & 18+175 \\\Leftrightarrow & \color{red}{-480} x& = & 193 \\\Leftrightarrow & x = \frac{193}{-480} & & \\\Leftrightarrow & x = \frac{-193}{480} & & \\ & V = \left\{ \frac{-193}{480} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{147x} +70 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & -210x-147x& = & 70-30 \\\Leftrightarrow & \color{red}{-357} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-357} & & \\\Leftrightarrow & x = \frac{-40}{357} & & \\ & V = \left\{ \frac{-40}{357} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{11})& = & -2x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{15}{11}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-45} & = & \color{red}{-66x} +88 \\\Leftrightarrow & 495x \color{red}{-45} \color{blue}{+45} \color{blue}{+66x} & = & \color{red}{-66x} +88 \color{blue}{+66x} \color{blue}{+45} \\\Leftrightarrow & 495x+66x& = & 88+45 \\\Leftrightarrow & \color{red}{561} x& = & 133 \\\Leftrightarrow & x = \frac{133}{561} & & \\ & V = \left\{ \frac{133}{561} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & 6x+\frac{8}{5} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 6x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{210}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{210x} +56 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{-210x} & = & \color{red}{210x} +56 \color{blue}{-210x} \color{blue}{+150} \\\Leftrightarrow & -630x-210x& = & 56+150 \\\Leftrightarrow & \color{red}{-840} x& = & 206 \\\Leftrightarrow & x = \frac{206}{-840} & & \\\Leftrightarrow & x = \frac{-103}{420} & & \\ & V = \left\{ \frac{-103}{420} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{7})& = & -3x+\frac{4}{5} \\\Leftrightarrow & -8x+\frac{20}{7}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+100} & = & \color{red}{-105x} +28 \\\Leftrightarrow & -280x \color{red}{+100} \color{blue}{-100} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{-100} \\\Leftrightarrow & -280x+105x& = & 28-100 \\\Leftrightarrow & \color{red}{-175} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{-175} & & \\\Leftrightarrow & x = \frac{72}{175} & & \\ & V = \left\{ \frac{72}{175} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{16}{7}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+48} & = & \color{red}{-63x} +70 \\\Leftrightarrow & 420x \color{red}{+48} \color{blue}{-48} \color{blue}{+63x} & = & \color{red}{-63x} +70 \color{blue}{+63x} \color{blue}{-48} \\\Leftrightarrow & 420x+63x& = & 70-48 \\\Leftrightarrow & \color{red}{483} x& = & 22 \\\Leftrightarrow & x = \frac{22}{483} & & \\ & V = \left\{ \frac{22}{483} \right\} & \\\end{align}\)