Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{4}{9})& = & 8x+\frac{6}{7} \\\Leftrightarrow & 35x+\frac{28}{9}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{2205}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 2205x \color{red}{+196} & = & \color{red}{504x} +54 \\\Leftrightarrow & 2205x \color{red}{+196} \color{blue}{-196} \color{blue}{-504x} & = & \color{red}{504x} +54 \color{blue}{-504x} \color{blue}{-196} \\\Leftrightarrow & 2205x-504x& = & 54-196 \\\Leftrightarrow & \color{red}{1701} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{1701} & & \\ & V = \left\{ \frac{-142}{1701} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 30x+\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{+108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & 1350x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & 1350x+315x& = & 50-108 \\\Leftrightarrow & \color{red}{1665} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{1665} & & \\ & V = \left\{ \frac{-58}{1665} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{3})& = & -2x+\frac{5}{3} \\\Leftrightarrow & 21x+\frac{28}{3}& = & -2x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{+28} & = & \color{red}{-6x} +5 \\\Leftrightarrow & 63x \color{red}{+28} \color{blue}{-28} \color{blue}{+6x} & = & \color{red}{-6x} +5 \color{blue}{+6x} \color{blue}{-28} \\\Leftrightarrow & 63x+6x& = & 5-28 \\\Leftrightarrow & \color{red}{69} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{69} & & \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{9})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -21x-\frac{35}{9}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{35}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-35} & = & \color{red}{72x} +24 \\\Leftrightarrow & -189x \color{red}{-35} \color{blue}{+35} \color{blue}{-72x} & = & \color{red}{72x} +24 \color{blue}{-72x} \color{blue}{+35} \\\Leftrightarrow & -189x-72x& = & 24+35 \\\Leftrightarrow & \color{red}{-261} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-261} & & \\\Leftrightarrow & x = \frac{-59}{261} & & \\ & V = \left\{ \frac{-59}{261} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{11})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -9x+\frac{15}{11}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{+105} & = & \color{red}{-385x} +33 \\\Leftrightarrow & -693x \color{red}{+105} \color{blue}{-105} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{-105} \\\Leftrightarrow & -693x+385x& = & 33-105 \\\Leftrightarrow & \color{red}{-308} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{-308} & & \\\Leftrightarrow & x = \frac{18}{77} & & \\ & V = \left\{ \frac{18}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{2})& = & 4x+\frac{9}{10} \\\Leftrightarrow & -15x+\frac{15}{2}& = & 4x+\frac{9}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+75} & = & \color{red}{40x} +9 \\\Leftrightarrow & -150x \color{red}{+75} \color{blue}{-75} \color{blue}{-40x} & = & \color{red}{40x} +9 \color{blue}{-40x} \color{blue}{-75} \\\Leftrightarrow & -150x-40x& = & 9-75 \\\Leftrightarrow & \color{red}{-190} x& = & -66 \\\Leftrightarrow & x = \frac{-66}{-190} & & \\\Leftrightarrow & x = \frac{33}{95} & & \\ & V = \left\{ \frac{33}{95} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{9})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-720}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -720x \color{red}{-64} & = & \color{red}{504x} +27 \\\Leftrightarrow & -720x \color{red}{-64} \color{blue}{+64} \color{blue}{-504x} & = & \color{red}{504x} +27 \color{blue}{-504x} \color{blue}{+64} \\\Leftrightarrow & -720x-504x& = & 27+64 \\\Leftrightarrow & \color{red}{-1224} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-1224} & & \\\Leftrightarrow & x = \frac{-91}{1224} & & \\ & V = \left\{ \frac{-91}{1224} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 18x-\frac{18}{11}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{-18} & = & \color{red}{-55x} +5 \\\Leftrightarrow & 198x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +5 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & 198x+55x& = & 5+18 \\\Leftrightarrow & \color{red}{253} x& = & 23 \\\Leftrightarrow & x = \frac{23}{253} & & \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & 4x+\frac{7}{11} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 4x+\frac{7}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{176}{ \color{blue}{44} }x+ \frac{28}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+165} & = & \color{red}{176x} +28 \\\Leftrightarrow & -660x \color{red}{+165} \color{blue}{-165} \color{blue}{-176x} & = & \color{red}{176x} +28 \color{blue}{-176x} \color{blue}{-165} \\\Leftrightarrow & -660x-176x& = & 28-165 \\\Leftrightarrow & \color{red}{-836} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{-836} & & \\\Leftrightarrow & x = \frac{137}{836} & & \\ & V = \left\{ \frac{137}{836} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{10})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -6x+\frac{9}{10}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+9} & = & \color{red}{-70x} +35 \\\Leftrightarrow & -60x \color{red}{+9} \color{blue}{-9} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-9} \\\Leftrightarrow & -60x+70x& = & 35-9 \\\Leftrightarrow & \color{red}{10} x& = & 26 \\\Leftrightarrow & x = \frac{26}{10} & & \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & 5x+\frac{7}{10} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{180}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 180x \color{red}{-48} & = & \color{red}{50x} +7 \\\Leftrightarrow & 180x \color{red}{-48} \color{blue}{+48} \color{blue}{-50x} & = & \color{red}{50x} +7 \color{blue}{-50x} \color{blue}{+48} \\\Leftrightarrow & 180x-50x& = & 7+48 \\\Leftrightarrow & \color{red}{130} x& = & 55 \\\Leftrightarrow & x = \frac{55}{130} & & \\\Leftrightarrow & x = \frac{11}{26} & & \\ & V = \left\{ \frac{11}{26} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -30x+\frac{30}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{147x} +56 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{-90} \\\Leftrightarrow & -630x-147x& = & 56-90 \\\Leftrightarrow & \color{red}{-777} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-777} & & \\\Leftrightarrow & x = \frac{34}{777} & & \\ & V = \left\{ \frac{34}{777} \right\} & \\\end{align}\)