Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & 4x+\frac{10}{9} \\\Leftrightarrow & 35x+\frac{21}{8}& = & 4x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2520}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{288}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2520x \color{red}{+189} & = & \color{red}{288x} +80 \\\Leftrightarrow & 2520x \color{red}{+189} \color{blue}{-189} \color{blue}{-288x} & = & \color{red}{288x} +80 \color{blue}{-288x} \color{blue}{-189} \\\Leftrightarrow & 2520x-288x& = & 80-189 \\\Leftrightarrow & \color{red}{2232} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{2232} & & \\ & V = \left\{ \frac{-109}{2232} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x- \frac{300}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{-300} & = & \color{red}{-550x} +99 \\\Leftrightarrow & -1320x \color{red}{-300} \color{blue}{+300} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{+300} \\\Leftrightarrow & -1320x+550x& = & 99+300 \\\Leftrightarrow & \color{red}{-770} x& = & 399 \\\Leftrightarrow & x = \frac{399}{-770} & & \\\Leftrightarrow & x = \frac{-57}{110} & & \\ & V = \left\{ \frac{-57}{110} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{11})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 12x+\frac{12}{11}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+108} & = & \color{red}{495x} +22 \\\Leftrightarrow & 1188x \color{red}{+108} \color{blue}{-108} \color{blue}{-495x} & = & \color{red}{495x} +22 \color{blue}{-495x} \color{blue}{-108} \\\Leftrightarrow & 1188x-495x& = & 22-108 \\\Leftrightarrow & \color{red}{693} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{693} & & \\ & V = \left\{ \frac{-86}{693} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{3})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 8x-\frac{20}{3}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-220} & = & \color{red}{-297x} +15 \\\Leftrightarrow & 264x \color{red}{-220} \color{blue}{+220} \color{blue}{+297x} & = & \color{red}{-297x} +15 \color{blue}{+297x} \color{blue}{+220} \\\Leftrightarrow & 264x+297x& = & 15+220 \\\Leftrightarrow & \color{red}{561} x& = & 235 \\\Leftrightarrow & x = \frac{235}{561} & & \\ & V = \left\{ \frac{235}{561} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{5})& = & -2x+\frac{3}{8} \\\Leftrightarrow & 9x-\frac{6}{5}& = & -2x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{360}{ \color{blue}{40} }x- \frac{48}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 360x \color{red}{-48} & = & \color{red}{-80x} +15 \\\Leftrightarrow & 360x \color{red}{-48} \color{blue}{+48} \color{blue}{+80x} & = & \color{red}{-80x} +15 \color{blue}{+80x} \color{blue}{+48} \\\Leftrightarrow & 360x+80x& = & 15+48 \\\Leftrightarrow & \color{red}{440} x& = & 63 \\\Leftrightarrow & x = \frac{63}{440} & & \\ & V = \left\{ \frac{63}{440} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{4})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 10x+\frac{25}{4}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x+ \frac{175}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{+175} & = & \color{red}{84x} +16 \\\Leftrightarrow & 280x \color{red}{+175} \color{blue}{-175} \color{blue}{-84x} & = & \color{red}{84x} +16 \color{blue}{-84x} \color{blue}{-175} \\\Leftrightarrow & 280x-84x& = & 16-175 \\\Leftrightarrow & \color{red}{196} x& = & -159 \\\Leftrightarrow & x = \frac{-159}{196} & & \\ & V = \left\{ \frac{-159}{196} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{6}{7}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-12} & = & \color{red}{-56x} +21 \\\Leftrightarrow & -210x \color{red}{-12} \color{blue}{+12} \color{blue}{+56x} & = & \color{red}{-56x} +21 \color{blue}{+56x} \color{blue}{+12} \\\Leftrightarrow & -210x+56x& = & 21+12 \\\Leftrightarrow & \color{red}{-154} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-154} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{11})& = & -7x+\frac{7}{3} \\\Leftrightarrow & 12x+\frac{6}{11}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+18} & = & \color{red}{-231x} +77 \\\Leftrightarrow & 396x \color{red}{+18} \color{blue}{-18} \color{blue}{+231x} & = & \color{red}{-231x} +77 \color{blue}{+231x} \color{blue}{-18} \\\Leftrightarrow & 396x+231x& = & 77-18 \\\Leftrightarrow & \color{red}{627} x& = & 59 \\\Leftrightarrow & x = \frac{59}{627} & & \\ & V = \left\{ \frac{59}{627} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{20}{3}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{+20} & = & \color{red}{15x} +10 \\\Leftrightarrow & -36x \color{red}{+20} \color{blue}{-20} \color{blue}{-15x} & = & \color{red}{15x} +10 \color{blue}{-15x} \color{blue}{-20} \\\Leftrightarrow & -36x-15x& = & 10-20 \\\Leftrightarrow & \color{red}{-51} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-51} & & \\\Leftrightarrow & x = \frac{10}{51} & & \\ & V = \left\{ \frac{10}{51} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -24x-\frac{12}{5}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1440}{ \color{blue}{60} }x- \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1440x \color{red}{-144} & = & \color{red}{300x} +35 \\\Leftrightarrow & -1440x \color{red}{-144} \color{blue}{+144} \color{blue}{-300x} & = & \color{red}{300x} +35 \color{blue}{-300x} \color{blue}{+144} \\\Leftrightarrow & -1440x-300x& = & 35+144 \\\Leftrightarrow & \color{red}{-1740} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-1740} & & \\\Leftrightarrow & x = \frac{-179}{1740} & & \\ & V = \left\{ \frac{-179}{1740} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -6x-\frac{15}{4}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-48}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -48x \color{red}{-30} & = & \color{red}{56x} +7 \\\Leftrightarrow & -48x \color{red}{-30} \color{blue}{+30} \color{blue}{-56x} & = & \color{red}{56x} +7 \color{blue}{-56x} \color{blue}{+30} \\\Leftrightarrow & -48x-56x& = & 7+30 \\\Leftrightarrow & \color{red}{-104} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-104} & & \\\Leftrightarrow & x = \frac{-37}{104} & & \\ & V = \left\{ \frac{-37}{104} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & 5x+\frac{3}{8} \\\Leftrightarrow & 18x-\frac{18}{5}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{720}{ \color{blue}{40} }x- \frac{144}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 720x \color{red}{-144} & = & \color{red}{200x} +15 \\\Leftrightarrow & 720x \color{red}{-144} \color{blue}{+144} \color{blue}{-200x} & = & \color{red}{200x} +15 \color{blue}{-200x} \color{blue}{+144} \\\Leftrightarrow & 720x-200x& = & 15+144 \\\Leftrightarrow & \color{red}{520} x& = & 159 \\\Leftrightarrow & x = \frac{159}{520} & & \\ & V = \left\{ \frac{159}{520} \right\} & \\\end{align}\)