Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{7})& = & 8x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{9}{7}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+99} & = & \color{red}{616x} +42 \\\Leftrightarrow & -1155x \color{red}{+99} \color{blue}{-99} \color{blue}{-616x} & = & \color{red}{616x} +42 \color{blue}{-616x} \color{blue}{-99} \\\Leftrightarrow & -1155x-616x& = & 42-99 \\\Leftrightarrow & \color{red}{-1771} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-1771} & & \\\Leftrightarrow & x = \frac{57}{1771} & & \\ & V = \left\{ \frac{57}{1771} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{2})& = & -9x+\frac{9}{11} \\\Leftrightarrow & -28x+\frac{35}{2}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-616}{ \color{blue}{22} }x+ \frac{385}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{18}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -616x \color{red}{+385} & = & \color{red}{-198x} +18 \\\Leftrightarrow & -616x \color{red}{+385} \color{blue}{-385} \color{blue}{+198x} & = & \color{red}{-198x} +18 \color{blue}{+198x} \color{blue}{-385} \\\Leftrightarrow & -616x+198x& = & 18-385 \\\Leftrightarrow & \color{red}{-418} x& = & -367 \\\Leftrightarrow & x = \frac{-367}{-418} & & \\\Leftrightarrow & x = \frac{367}{418} & & \\ & V = \left\{ \frac{367}{418} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{9})& = & -8x+\frac{10}{3} \\\Leftrightarrow & 21x-\frac{14}{9}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{-14} & = & \color{red}{-72x} +30 \\\Leftrightarrow & 189x \color{red}{-14} \color{blue}{+14} \color{blue}{+72x} & = & \color{red}{-72x} +30 \color{blue}{+72x} \color{blue}{+14} \\\Leftrightarrow & 189x+72x& = & 30+14 \\\Leftrightarrow & \color{red}{261} x& = & 44 \\\Leftrightarrow & x = \frac{44}{261} & & \\ & V = \left\{ \frac{44}{261} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 8x-\frac{16}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-48} & = & \color{red}{165x} +44 \\\Leftrightarrow & 264x \color{red}{-48} \color{blue}{+48} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{+48} \\\Leftrightarrow & 264x-165x& = & 44+48 \\\Leftrightarrow & \color{red}{99} x& = & 92 \\\Leftrightarrow & x = \frac{92}{99} & & \\ & V = \left\{ \frac{92}{99} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{2})& = & -3x+\frac{7}{11} \\\Leftrightarrow & -25x-\frac{15}{2}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-550}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{14}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -550x \color{red}{-165} & = & \color{red}{-66x} +14 \\\Leftrightarrow & -550x \color{red}{-165} \color{blue}{+165} \color{blue}{+66x} & = & \color{red}{-66x} +14 \color{blue}{+66x} \color{blue}{+165} \\\Leftrightarrow & -550x+66x& = & 14+165 \\\Leftrightarrow & \color{red}{-484} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-484} & & \\\Leftrightarrow & x = \frac{-179}{484} & & \\ & V = \left\{ \frac{-179}{484} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -20x-\frac{8}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{-8} & = & \color{red}{-99x} +6 \\\Leftrightarrow & -220x \color{red}{-8} \color{blue}{+8} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{+8} \\\Leftrightarrow & -220x+99x& = & 6+8 \\\Leftrightarrow & \color{red}{-121} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-121} & & \\\Leftrightarrow & x = \frac{-14}{121} & & \\ & V = \left\{ \frac{-14}{121} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x+ \frac{216}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{+216} & = & \color{red}{-315x} +50 \\\Leftrightarrow & 810x \color{red}{+216} \color{blue}{-216} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-216} \\\Leftrightarrow & 810x+315x& = & 50-216 \\\Leftrightarrow & \color{red}{1125} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{1125} & & \\ & V = \left\{ \frac{-166}{1125} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{8})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -28x-\frac{21}{8}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{-21} & = & \color{red}{56x} +18 \\\Leftrightarrow & -224x \color{red}{-21} \color{blue}{+21} \color{blue}{-56x} & = & \color{red}{56x} +18 \color{blue}{-56x} \color{blue}{+21} \\\Leftrightarrow & -224x-56x& = & 18+21 \\\Leftrightarrow & \color{red}{-280} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-280} & & \\\Leftrightarrow & x = \frac{-39}{280} & & \\ & V = \left\{ \frac{-39}{280} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{8})& = & -8x+\frac{2}{9} \\\Leftrightarrow & 15x-\frac{15}{8}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1080}{ \color{blue}{72} }x- \frac{135}{ \color{blue}{72} })& = & (\frac{-576}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1080x \color{red}{-135} & = & \color{red}{-576x} +16 \\\Leftrightarrow & 1080x \color{red}{-135} \color{blue}{+135} \color{blue}{+576x} & = & \color{red}{-576x} +16 \color{blue}{+576x} \color{blue}{+135} \\\Leftrightarrow & 1080x+576x& = & 16+135 \\\Leftrightarrow & \color{red}{1656} x& = & 151 \\\Leftrightarrow & x = \frac{151}{1656} & & \\ & V = \left\{ \frac{151}{1656} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{2})& = & -5x+\frac{5}{8} \\\Leftrightarrow & -12x+\frac{9}{2}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{+36} & = & \color{red}{-40x} +5 \\\Leftrightarrow & -96x \color{red}{+36} \color{blue}{-36} \color{blue}{+40x} & = & \color{red}{-40x} +5 \color{blue}{+40x} \color{blue}{-36} \\\Leftrightarrow & -96x+40x& = & 5-36 \\\Leftrightarrow & \color{red}{-56} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-56} & & \\\Leftrightarrow & x = \frac{31}{56} & & \\ & V = \left\{ \frac{31}{56} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -9x+\frac{6}{7}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-567}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -567x \color{red}{+54} & = & \color{red}{315x} +28 \\\Leftrightarrow & -567x \color{red}{+54} \color{blue}{-54} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{-54} \\\Leftrightarrow & -567x-315x& = & 28-54 \\\Leftrightarrow & \color{red}{-882} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-882} & & \\\Leftrightarrow & x = \frac{13}{441} & & \\ & V = \left\{ \frac{13}{441} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{9})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 10x-\frac{25}{9}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{360}{ \color{blue}{36} }x- \frac{100}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 360x \color{red}{-100} & = & \color{red}{-108x} +27 \\\Leftrightarrow & 360x \color{red}{-100} \color{blue}{+100} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{+100} \\\Leftrightarrow & 360x+108x& = & 27+100 \\\Leftrightarrow & \color{red}{468} x& = & 127 \\\Leftrightarrow & x = \frac{127}{468} & & \\ & V = \left\{ \frac{127}{468} \right\} & \\\end{align}\)