Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{-50x} +45 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +45 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & 60x+50x& = & 45+24 \\\Leftrightarrow & \color{red}{110} x& = & 69 \\\Leftrightarrow & x = \frac{69}{110} & & \\ & V = \left\{ \frac{69}{110} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 10x+\frac{4}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{+8} & = & \color{red}{-70x} +15 \\\Leftrightarrow & 100x \color{red}{+8} \color{blue}{-8} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{-8} \\\Leftrightarrow & 100x+70x& = & 15-8 \\\Leftrightarrow & \color{red}{170} x& = & 7 \\\Leftrightarrow & x = \frac{7}{170} & & \\ & V = \left\{ \frac{7}{170} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{3})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 10x-\frac{8}{3}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-88} & = & \color{red}{-99x} +24 \\\Leftrightarrow & 330x \color{red}{-88} \color{blue}{+88} \color{blue}{+99x} & = & \color{red}{-99x} +24 \color{blue}{+99x} \color{blue}{+88} \\\Leftrightarrow & 330x+99x& = & 24+88 \\\Leftrightarrow & \color{red}{429} x& = & 112 \\\Leftrightarrow & x = \frac{112}{429} & & \\ & V = \left\{ \frac{112}{429} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & -9x+\frac{7}{8} \\\Leftrightarrow & -4x-\frac{6}{7}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-224}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -224x \color{red}{-48} & = & \color{red}{-504x} +49 \\\Leftrightarrow & -224x \color{red}{-48} \color{blue}{+48} \color{blue}{+504x} & = & \color{red}{-504x} +49 \color{blue}{+504x} \color{blue}{+48} \\\Leftrightarrow & -224x+504x& = & 49+48 \\\Leftrightarrow & \color{red}{280} x& = & 97 \\\Leftrightarrow & x = \frac{97}{280} & & \\ & V = \left\{ \frac{97}{280} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{9})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -12x+\frac{8}{9}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+56} & = & \color{red}{315x} +72 \\\Leftrightarrow & -756x \color{red}{+56} \color{blue}{-56} \color{blue}{-315x} & = & \color{red}{315x} +72 \color{blue}{-315x} \color{blue}{-56} \\\Leftrightarrow & -756x-315x& = & 72-56 \\\Leftrightarrow & \color{red}{-1071} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-1071} & & \\\Leftrightarrow & x = \frac{-16}{1071} & & \\ & V = \left\{ \frac{-16}{1071} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+90} & = & \color{red}{385x} +44 \\\Leftrightarrow & -1650x \color{red}{+90} \color{blue}{-90} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-90} \\\Leftrightarrow & -1650x-385x& = & 44-90 \\\Leftrightarrow & \color{red}{-2035} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-2035} & & \\\Leftrightarrow & x = \frac{46}{2035} & & \\ & V = \left\{ \frac{46}{2035} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & -7x+\frac{9}{5} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-150} & = & \color{red}{-245x} +63 \\\Leftrightarrow & 1050x \color{red}{-150} \color{blue}{+150} \color{blue}{+245x} & = & \color{red}{-245x} +63 \color{blue}{+245x} \color{blue}{+150} \\\Leftrightarrow & 1050x+245x& = & 63+150 \\\Leftrightarrow & \color{red}{1295} x& = & 213 \\\Leftrightarrow & x = \frac{213}{1295} & & \\ & V = \left\{ \frac{213}{1295} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{10})& = & 9x+\frac{7}{9} \\\Leftrightarrow & 35x+\frac{21}{10}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{3150}{ \color{blue}{90} }x+ \frac{189}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{70}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 3150x \color{red}{+189} & = & \color{red}{810x} +70 \\\Leftrightarrow & 3150x \color{red}{+189} \color{blue}{-189} \color{blue}{-810x} & = & \color{red}{810x} +70 \color{blue}{-810x} \color{blue}{-189} \\\Leftrightarrow & 3150x-810x& = & 70-189 \\\Leftrightarrow & \color{red}{2340} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{2340} & & \\ & V = \left\{ \frac{-119}{2340} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{5})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -21x-\frac{28}{5}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{120x} +20 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{-120x} & = & \color{red}{120x} +20 \color{blue}{-120x} \color{blue}{+84} \\\Leftrightarrow & -315x-120x& = & 20+84 \\\Leftrightarrow & \color{red}{-435} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-435} & & \\\Leftrightarrow & x = \frac{-104}{435} & & \\ & V = \left\{ \frac{-104}{435} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & 4x+\frac{2}{5} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 4x+\frac{2}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{8}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+75} & = & \color{red}{80x} +8 \\\Leftrightarrow & -300x \color{red}{+75} \color{blue}{-75} \color{blue}{-80x} & = & \color{red}{80x} +8 \color{blue}{-80x} \color{blue}{-75} \\\Leftrightarrow & -300x-80x& = & 8-75 \\\Leftrightarrow & \color{red}{-380} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-380} & & \\\Leftrightarrow & x = \frac{67}{380} & & \\ & V = \left\{ \frac{67}{380} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-18} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -132x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & -132x+55x& = & 6+18 \\\Leftrightarrow & \color{red}{-77} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-77} & & \\\Leftrightarrow & x = \frac{-24}{77} & & \\ & V = \left\{ \frac{-24}{77} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1008}{ \color{blue}{42} }x+ \frac{180}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1008x \color{red}{+180} & = & \color{red}{-210x} +49 \\\Leftrightarrow & 1008x \color{red}{+180} \color{blue}{-180} \color{blue}{+210x} & = & \color{red}{-210x} +49 \color{blue}{+210x} \color{blue}{-180} \\\Leftrightarrow & 1008x+210x& = & 49-180 \\\Leftrightarrow & \color{red}{1218} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{1218} & & \\ & V = \left\{ \frac{-131}{1218} \right\} & \\\end{align}\)