Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & 3x+\frac{7}{8} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x+ \frac{128}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{+128} & = & \color{red}{168x} +49 \\\Leftrightarrow & -1120x \color{red}{+128} \color{blue}{-128} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{-128} \\\Leftrightarrow & -1120x-168x& = & 49-128 \\\Leftrightarrow & \color{red}{-1288} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-1288} & & \\\Leftrightarrow & x = \frac{79}{1288} & & \\ & V = \left\{ \frac{79}{1288} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{11})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 18x-\frac{24}{11}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{792}{ \color{blue}{44} }x- \frac{96}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 792x \color{red}{-96} & = & \color{red}{-220x} +99 \\\Leftrightarrow & 792x \color{red}{-96} \color{blue}{+96} \color{blue}{+220x} & = & \color{red}{-220x} +99 \color{blue}{+220x} \color{blue}{+96} \\\Leftrightarrow & 792x+220x& = & 99+96 \\\Leftrightarrow & \color{red}{1012} x& = & 195 \\\Leftrightarrow & x = \frac{195}{1012} & & \\ & V = \left\{ \frac{195}{1012} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{5})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -9x+\frac{9}{5}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{-100x} +15 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{+100x} & = & \color{red}{-100x} +15 \color{blue}{+100x} \color{blue}{-36} \\\Leftrightarrow & -180x+100x& = & 15-36 \\\Leftrightarrow & \color{red}{-80} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-80} & & \\\Leftrightarrow & x = \frac{21}{80} & & \\ & V = \left\{ \frac{21}{80} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{16}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{144}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+144} & = & \color{red}{315x} +70 \\\Leftrightarrow & -756x \color{red}{+144} \color{blue}{-144} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{-144} \\\Leftrightarrow & -756x-315x& = & 70-144 \\\Leftrightarrow & \color{red}{-1071} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-1071} & & \\\Leftrightarrow & x = \frac{74}{1071} & & \\ & V = \left\{ \frac{74}{1071} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{11})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{10}{11}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-20} & = & \color{red}{198x} +77 \\\Leftrightarrow & 440x \color{red}{-20} \color{blue}{+20} \color{blue}{-198x} & = & \color{red}{198x} +77 \color{blue}{-198x} \color{blue}{+20} \\\Leftrightarrow & 440x-198x& = & 77+20 \\\Leftrightarrow & \color{red}{242} x& = & 97 \\\Leftrightarrow & x = \frac{97}{242} & & \\ & V = \left\{ \frac{97}{242} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{9})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 10x+\frac{10}{9}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+70} & = & \color{red}{-189x} +18 \\\Leftrightarrow & 630x \color{red}{+70} \color{blue}{-70} \color{blue}{+189x} & = & \color{red}{-189x} +18 \color{blue}{+189x} \color{blue}{-70} \\\Leftrightarrow & 630x+189x& = & 18-70 \\\Leftrightarrow & \color{red}{819} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{819} & & \\\Leftrightarrow & x = \frac{-4}{63} & & \\ & V = \left\{ \frac{-4}{63} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -9x-\frac{9}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-126}{ \color{blue}{14} }x- \frac{18}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{70x} +21 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{+18} \\\Leftrightarrow & -126x-70x& = & 21+18 \\\Leftrightarrow & \color{red}{-196} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-196} & & \\\Leftrightarrow & x = \frac{-39}{196} & & \\ & V = \left\{ \frac{-39}{196} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{7})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{20}{7}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+100} & = & \color{red}{175x} +56 \\\Leftrightarrow & 420x \color{red}{+100} \color{blue}{-100} \color{blue}{-175x} & = & \color{red}{175x} +56 \color{blue}{-175x} \color{blue}{-100} \\\Leftrightarrow & 420x-175x& = & 56-100 \\\Leftrightarrow & \color{red}{245} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{245} & & \\ & V = \left\{ \frac{-44}{245} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{9})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{8}{9}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-8} & = & \color{red}{81x} +6 \\\Leftrightarrow & -72x \color{red}{-8} \color{blue}{+8} \color{blue}{-81x} & = & \color{red}{81x} +6 \color{blue}{-81x} \color{blue}{+8} \\\Leftrightarrow & -72x-81x& = & 6+8 \\\Leftrightarrow & \color{red}{-153} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-153} & & \\\Leftrightarrow & x = \frac{-14}{153} & & \\ & V = \left\{ \frac{-14}{153} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 12x+\frac{15}{8}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{96}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 96x \color{red}{+15} & = & \color{red}{56x} +3 \\\Leftrightarrow & 96x \color{red}{+15} \color{blue}{-15} \color{blue}{-56x} & = & \color{red}{56x} +3 \color{blue}{-56x} \color{blue}{-15} \\\Leftrightarrow & 96x-56x& = & 3-15 \\\Leftrightarrow & \color{red}{40} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{40} & & \\\Leftrightarrow & x = \frac{-3}{10} & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 24x+\frac{12}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{336}{ \color{blue}{14} }x+ \frac{24}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 336x \color{red}{+24} & = & \color{red}{-70x} +21 \\\Leftrightarrow & 336x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & 336x+70x& = & 21-24 \\\Leftrightarrow & \color{red}{406} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{406} & & \\ & V = \left\{ \frac{-3}{406} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{7})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 18x-\frac{24}{7}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1134}{ \color{blue}{63} }x- \frac{216}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1134x \color{red}{-216} & = & \color{red}{441x} +70 \\\Leftrightarrow & 1134x \color{red}{-216} \color{blue}{+216} \color{blue}{-441x} & = & \color{red}{441x} +70 \color{blue}{-441x} \color{blue}{+216} \\\Leftrightarrow & 1134x-441x& = & 70+216 \\\Leftrightarrow & \color{red}{693} x& = & 286 \\\Leftrightarrow & x = \frac{286}{693} & & \\\Leftrightarrow & x = \frac{26}{63} & & \\ & V = \left\{ \frac{26}{63} \right\} & \\\end{align}\)