Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{11})& = & -9x+\frac{8}{7} \\\Leftrightarrow & -8x-\frac{6}{11}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-42} & = & \color{red}{-693x} +88 \\\Leftrightarrow & -616x \color{red}{-42} \color{blue}{+42} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{+42} \\\Leftrightarrow & -616x+693x& = & 88+42 \\\Leftrightarrow & \color{red}{77} x& = & 130 \\\Leftrightarrow & x = \frac{130}{77} & & \\ & V = \left\{ \frac{130}{77} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{2}{11} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{-231} & = & \color{red}{-264x} +16 \\\Leftrightarrow & -1232x \color{red}{-231} \color{blue}{+231} \color{blue}{+264x} & = & \color{red}{-264x} +16 \color{blue}{+264x} \color{blue}{+231} \\\Leftrightarrow & -1232x+264x& = & 16+231 \\\Leftrightarrow & \color{red}{-968} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-968} & & \\\Leftrightarrow & x = \frac{-247}{968} & & \\ & V = \left\{ \frac{-247}{968} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{-270} & = & \color{red}{-315x} +70 \\\Leftrightarrow & -1512x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +70 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & -1512x+315x& = & 70+270 \\\Leftrightarrow & \color{red}{-1197} x& = & 340 \\\Leftrightarrow & x = \frac{340}{-1197} & & \\\Leftrightarrow & x = \frac{-340}{1197} & & \\ & V = \left\{ \frac{-340}{1197} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -9x-\frac{9}{10}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-990}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -990x \color{red}{-99} & = & \color{red}{550x} +60 \\\Leftrightarrow & -990x \color{red}{-99} \color{blue}{+99} \color{blue}{-550x} & = & \color{red}{550x} +60 \color{blue}{-550x} \color{blue}{+99} \\\Leftrightarrow & -990x-550x& = & 60+99 \\\Leftrightarrow & \color{red}{-1540} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-1540} & & \\\Leftrightarrow & x = \frac{-159}{1540} & & \\ & V = \left\{ \frac{-159}{1540} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -3x+\frac{10}{11} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+132} & = & \color{red}{-165x} +50 \\\Leftrightarrow & -440x \color{red}{+132} \color{blue}{-132} \color{blue}{+165x} & = & \color{red}{-165x} +50 \color{blue}{+165x} \color{blue}{-132} \\\Leftrightarrow & -440x+165x& = & 50-132 \\\Leftrightarrow & \color{red}{-275} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-275} & & \\\Leftrightarrow & x = \frac{82}{275} & & \\ & V = \left\{ \frac{82}{275} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{5})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 10x-\frac{6}{5}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{-18} & = & \color{red}{-135x} +20 \\\Leftrightarrow & 150x \color{red}{-18} \color{blue}{+18} \color{blue}{+135x} & = & \color{red}{-135x} +20 \color{blue}{+135x} \color{blue}{+18} \\\Leftrightarrow & 150x+135x& = & 20+18 \\\Leftrightarrow & \color{red}{285} x& = & 38 \\\Leftrightarrow & x = \frac{38}{285} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{5})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -6x+\frac{6}{5}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+42} & = & \color{red}{-245x} +15 \\\Leftrightarrow & -210x \color{red}{+42} \color{blue}{-42} \color{blue}{+245x} & = & \color{red}{-245x} +15 \color{blue}{+245x} \color{blue}{-42} \\\Leftrightarrow & -210x+245x& = & 15-42 \\\Leftrightarrow & \color{red}{35} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{35} & & \\ & V = \left\{ \frac{-27}{35} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{10})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{9}{10}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{20}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{+27} & = & \color{red}{210x} +20 \\\Leftrightarrow & 180x \color{red}{+27} \color{blue}{-27} \color{blue}{-210x} & = & \color{red}{210x} +20 \color{blue}{-210x} \color{blue}{-27} \\\Leftrightarrow & 180x-210x& = & 20-27 \\\Leftrightarrow & \color{red}{-30} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-30} & & \\\Leftrightarrow & x = \frac{7}{30} & & \\ & V = \left\{ \frac{7}{30} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & 3x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{15}{4}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{-75} & = & \color{red}{60x} +16 \\\Leftrightarrow & -400x \color{red}{-75} \color{blue}{+75} \color{blue}{-60x} & = & \color{red}{60x} +16 \color{blue}{-60x} \color{blue}{+75} \\\Leftrightarrow & -400x-60x& = & 16+75 \\\Leftrightarrow & \color{red}{-460} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-460} & & \\\Leftrightarrow & x = \frac{-91}{460} & & \\ & V = \left\{ \frac{-91}{460} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{2})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -10x-\frac{25}{2}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{175}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-175} & = & \color{red}{98x} +16 \\\Leftrightarrow & -140x \color{red}{-175} \color{blue}{+175} \color{blue}{-98x} & = & \color{red}{98x} +16 \color{blue}{-98x} \color{blue}{+175} \\\Leftrightarrow & -140x-98x& = & 16+175 \\\Leftrightarrow & \color{red}{-238} x& = & 191 \\\Leftrightarrow & x = \frac{191}{-238} & & \\\Leftrightarrow & x = \frac{-191}{238} & & \\ & V = \left\{ \frac{-191}{238} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{3})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 25x-\frac{20}{3}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{-220} & = & \color{red}{-231x} +24 \\\Leftrightarrow & 825x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +24 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & 825x+231x& = & 24+220 \\\Leftrightarrow & \color{red}{1056} x& = & 244 \\\Leftrightarrow & x = \frac{244}{1056} & & \\\Leftrightarrow & x = \frac{61}{264} & & \\ & V = \left\{ \frac{61}{264} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{11})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{+40} & = & \color{red}{308x} +55 \\\Leftrightarrow & -440x \color{red}{+40} \color{blue}{-40} \color{blue}{-308x} & = & \color{red}{308x} +55 \color{blue}{-308x} \color{blue}{-40} \\\Leftrightarrow & -440x-308x& = & 55-40 \\\Leftrightarrow & \color{red}{-748} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-748} & & \\\Leftrightarrow & x = \frac{-15}{748} & & \\ & V = \left\{ \frac{-15}{748} \right\} & \\\end{align}\)